{"id":861,"date":"2016-09-19T18:37:33","date_gmt":"2016-09-19T23:37:33","guid":{"rendered":"http:\/\/www.marshall.edu\/math\/?page_id=861"},"modified":"2026-01-21T09:28:41","modified_gmt":"2026-01-21T14:28:41","slug":"colloquium","status":"publish","type":"page","link":"https:\/\/www.marshall.edu\/math\/colloquium\/","title":{"rendered":"Math Colloquium"},"content":{"rendered":"

Each semester the Department of Mathematics & Physics offers colloquium talks on a variety of mathematical topics. The department also hosts the Advanced Research Initiative<\/a> series, featuring a distinguished guest speaker giving two talks.<\/p>\n \n \n \n \n

\n 2026 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2026 Spring Math Colloquia<\/h2>\n
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January 28 <\/b>Virtual, 1:00pm<\/p>\n<\/div>\n

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Dr. Tomas Miquel Rodriguez (Kenyon College)
\nSquare roots of weighted shifts of multiplicity two<\/p>\n

Abstract: <\/em>A weighted shift of multiplicity two with weight sequency {\u03bbn<\/sub>} is a bounded linear operator T on l2<\/sup> such that<\/p>\n

T(x0<\/sub>, x1<\/sub>, x2<\/sub>, . . .) = (0, 0, \u03bb0<\/sub>x0<\/sub>, \u03bb1<\/sub>x1<\/sub>, \u03bb2<\/sub>x2<\/sub>, . . .),<\/p>\n

for all n>=0 where \u03bbn<\/sub> \u2208 C. The square root of T is a bounded operator Q such that Q2<\/sup> = T. It is known that the weighted shift of multiplicity one do not have any square root. This is not the case when we consider a weighted shift T of multiplicity two. In this talk, we present necessary and sufficient conditions on the weight sequence so that the set of square roots of T is non-empty. We show that when such conditions are satisfied, the set contains a certain special class of operators. We also present a complete description of all operators in the set of square roots of T.<\/p>\n

Joint work with Chanaka Kottegoda and Trieu Le<\/p>\n<\/div>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2025 Fall\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
\n \n

2025 Fall Math Colloquia<\/h2>\n
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November 5 <\/b>Smith Hall 621 & Virtual, 1:00pm<\/p>\n<\/div>\n

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Chloe’ Napier (Marshall University)
\nExtensions in the Preprojective Algebras<\/span><\/p>\n

Abstract: <\/em>In 2001, Fomin and Zelevinsky introduced cluster algebras as a way to study total positivity. These objects lie within the intersection of algebra and combinatorics. One use of cluster algebras is that they can be used to describe many important algebraic spaces by associating a certain type of graph to them and then group its elements into n-tuples. Though these constructions can be very algebraic, in this work, we look at these spaces through a more combinatorial lense. To do this, we model objects of our space with tableaux and lattice paths. We are aiming to find a combinatorial description for when elements can be in the same n-tuple. In this talk, we will discuss the background of the Grassmannian and Richardson varieties, introduce the combinatorics for studying these varieties and provide answers to our overarching question.<\/span><\/p>\n<\/div>\n

October 16 <\/b>Smith Hall 624 & Virtual, 5:00pm<\/p>\n<\/div>\n

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Dr. Nick Wintz (Radford University)
\nLinear quadratic pursuit\u2013evasion games on time scales<\/span><\/p>\n

Abstract: <\/em>In this paper, we unify and extend the linear quadratic pursuit-evasion games to dynamic equations on time scales. A mixed strategy for a single pursuer and evader is studied in two settings. In the open-loop setting, the corresponding controls are expressed in terms of a zero-input difference. In the closed-loop setting, the corresponding controls require a mixing feedback term when rewriting the system in extended state form. Finally, we offer a numerical simulation.<\/p>\n<\/div>\n<\/div>\n

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September 17 <\/b>Smith Hall 154 & Virtual, 1:00pm<\/p>\n<\/div>\n

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Dr. Stephen Deterding (Marshall University)
\nEpic Math Battle of History: Tartaglia, Cardano, and the Discovery of Imaginary Numbers<\/span><\/p>\n

Abstract: <\/em>In 1546 the mathematician Niccol’o Tartaglia accused Girolamo Cardano, a doctor and mathematician, of having published in one of his books a result that Tartaglia had shared with him under the condition that he never reveal it to anyone else. Thus began what is arguably the most infamous feud in all mathematics. Over the next year Tartaglia and Cardano’s pupil, Lodovico Ferrari, who stepped up to defend him, would write several open letters to each other arguing their position in this controversy. Ultimately, a lively debate would be held between Tartaglia and Ferrari to resolve their dispute.<\/p>\n

<\/div>\n
From this backdrop of betrayal and feuding emerged some of the greatest mathematical discoveries, the cubic formula, the quartic formula, and imaginary numbers. In this talk, we will trace the history of the Tartaglia-Cardano controversy from its beginning, examine the mathematics that emerged as a result, and demonstrate how the controversy resulted in the discovery of imaginary numbers as an indispensable part of mathematics.<\/div>\n<\/div>\n

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August 20 <\/b>Smith Hall 516 & Virtual, 1:00pm<\/p>\n<\/div>\n

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Dr. Shalmali<\/span> Bandyopadhyay<\/span> (University of Tennessee at Martin)
\nThe Coexistence Paradox: When Bigger Isn’t Always Better in Fragmented Landscape<\/i>s<\/p>\n

Abstract: <\/em>We analyse the diffusive Lotka-Volterra competition model in fragmented landscapes using Robin boundary conditions to capture realistic species responses at patch-matrix interfaces. Through eigenvalue analysis, sub-supersolution methods, and bifurcation theory, we establish existence and uniqueness of coexistence states across different competition regimes. Our key finding reveals that in semi strong competition cases, coexistence occurs only within finite patch size intervals\u2014requiring patches that are neither too small nor too large\u2014which fundamentally challenges classical results where larger patches always favour coexistence. Using computational methods for the asymmetric case, we demonstrate that this phenomenon emerges from dispersal-competition trade offs where one species excels at colonizing smaller patches while its competitor dominates direct resource competition, suggesting profound implications for conservation design in fragmented landscapes.<\/p>\n<\/div>\n

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\n 2025 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2025 Spring Math Colloquia<\/h2>\n
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April 25<\/b>\u00a0Smith Hall 518 & Virtual, 1:00pm<\/p>\n

Dr. Andrej Gendiar (Slovak Academy of Sciences)
\nEntanglement in Tensor Networks<\/p>\n

Abstract:<\/em> Tensor Networks form a special class of variational quantum states widely used to study strongly correlated many-body systems. Originally developed from one-dimensional Matrix Product States\u2014the foundation of the Density Matrix Renormalization Group\u2014these methods have since been extended to compute ground and excited states in higher-dimensional systems.
\nIn this work, we explore the mathematical foundations of Tensor Networks, emphasizing their connection to the maximization of quantum entanglement. Key principles are illustrated through simple, instructive examples. Leveraging the quantum-classical correspondence via imaginary time evolution, we analyze two equivalent representations of Tensor Networks:<\/p>\n

1. the vertex representation, typically used in describing quantum states, and
\n2. the weight representation, familiar from classical statistical mechanics.<\/p>\n

We examine two-dimensional classical spin models with equivalent partition functions under both representations. Although these two approaches yield identical observables and correlation functions, we find that the entanglement entropy is consistently lower in the vertex representation\u2014across both finite and infinite systems. This reduction in entanglement holds universally, regardless of the spin-lattice model, the number of spin degrees of freedom, or the underlying lattice geometry. To understand this persistent discrepancy, we investigate various types of Tensor Network structures across a broad range of spin Hamiltonians and phase transition scenarios.<\/p>\n

April 11<\/b>\u00a0Smith Hall 518 & Virtual, 1:00pm<\/p>\n

Dinh-Liem Nguyen (Kansas State University)
\nDirect reconstruction methods for inverse source and scattering problems with single-frequency data<\/p>\n

Abstract:<\/em> Inverse source and scattering problems involve determining an unknown object from indirect measurements associated with the object. These problems, which arise in a variety of applications such as nondestructive testing, radar, medical imaging, and geophysical exploration, have been an active research topic in the mathematics, engineering, and physics communities for several decades. However, they are highly ill-posed and nonlinear, posing significant challenges in developing efficient numerical methods for their solution.<\/p>\n

In this talk, we will present our recent results in developing sampling type methods with novel imaging functions for solving inverse source and scattering problems using boundary data at a single frequency. Theoretical justifications and numerical simulations of the proposed method will be discussed. Our approach is non-iterative, computationally efficient, and straightforward to implement. This talk is based on joint work with Isaac Harris, Tran Lan, and Thu Le.<\/p>\n

March 27<\/b> Smith Hall 518 & Virtual, 1:00pm<\/p>\n

Anna Mummert (Marshall University)
\nA New Proof of the Pythagorean Theorems<\/p>\n

Abstract:<\/em> The Pythagorean Theorem has been proven in numerous ways throughout history, yet new insights continue to emerge. In 2023, high school students Jackson and Johnson presented a novel proof using a blend of geometry, algebra, and trigonometry. Their approach leverages geometric constructions, similarities, geometric series, and the Law of Sines to establish the theorem. In this talk will walk through their proof step by step, showcasing the power of creative reasoning in mathematical discovery. No advanced prerequisites are needed this talk will be accessible to all undergraduate students.<\/p>\n

February 19<\/b> Smith Hall 516 & Virtual, 1:00pm<\/p>\n

Chanaka Kottegoda (Marshall U)
\nResurgence of Large Influenza A (H1N1) Outbreaks: Modeling the Interplay of Dynamic Infection, Loss of Immunity, and Vaccination Rates<\/p>\n

Abstract:<\/em> The 2009 epidemic outbreaks caused by the H1N1pdm09 influenza A virus strain had a profound global impact, resulting in millions of cases and hundreds of thousands of deaths worldwide. After the initial outbreaks, many regions experienced subsequent waves of H1N1, driven by environmental conditions and loss of immunity, among other elements. More dramatically, several locations witnessed large resurgent H1N1 outbreaks, and the underlying factors that contributed to such severe resurgence remain poorly understood. In this study, we investigate the factors contributing to large resurgent outbreaks of the H1N1pdm09 influenza A virus following the initial 2009 pandemic. Using a mechanistic model, we explore the roles of seasonal climate variations, vaccination coverage, and immunity loss due to viral mutations in driving subsequent outbreaks. The study provides insights into the complex interplay between these factors by identifying key parametric conditions for resurgence. Model simulations and historical data analysis from eight countries reveal oscillations in infection rates and immunity loss. The findings emphasize the importance of understanding these interactions to develop effective strategies for controlling H1N1 outbreaks.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2024 Fall\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2024 Fall Math Colloquia<\/h2>\n
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November 20<\/b> Smith Hall 518 & Virtual, 1:00pm<\/p>\n

Trung Truong (Marshall U)
\nAdvances in Numerical Methods for Inverse Scattering<\/p>\n

Abstract:<\/em> Inverse scattering problems arise from various applications in real life: radar technology, geophysical exploration, medical imaging, and non-destructive testing, to name a few. These problems aim to detect, locate, image, or even determine physical parameters of an unknown object by analyzing how the object scatters waves. Over the past few decades, there have been a great number of numerical methods studied by not only mathematicians, but also physicists and engineers to solve inverse scattering problems. In this talk, we will have a glance at some of the most well-known methods in this field. Their theoretical foundation, numerical implementation, and some related open questions will be presented.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2023 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2023 Spring Math Colloquia<\/h2>\n
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February 27<\/b> Smith Hall 518 & Virtual, 4:00pm<\/p>\n

Stephen Deterding (Marshall U)
\nRoadrunner Sets and Swiss Cheeses<\/p>\n

Abstract:<\/em> Roadrunner sets and Swiss cheeses are special sets in the complex plane that are used to solve problems in approximation theory.\u00a0 In this talk we will examine one such problem, the question of determining when every sequence of derivatives on a compact set converges at a boundary point of the set.\u00a0 We will demonstrate how to construct roadrunner sets and Swiss cheeses and explain why these sets provide an answer to this problem.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2021 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2021 Spring Math Colloquia<\/h2>\n
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March 17<\/b> Virtual, 4:00pm<\/p>\n

Brook Brown (Ohio U), Kelly Bubp, PhD (Frostburg State U), Allyson Hallman-Thrusher, PhD (Ohio U)
\nInquiry-Based Learning in Calculus: Successes & Challenges<\/p>\n

Abstract:<\/em> We will describe the implementation over three semesters of an inquiry-based learning (IBL) approach to instruction in Calculus I at our university. We analyzed the effectiveness of the IBL approach using a standards-based final exam and a survey which included both open-ended and Likert scale items to collect student feedback on various aspects of the course. Based on survey results each semester, we revised the implementation of IBL-Calculus to address student concerns and difficulties. In this talk, we will report on student performance gains, affective and disposition gains, and the students\u2019 reactions to the course structure and their willingness to another IBL course. Students in IBL-Calculus outperformed peers in lecture-based Calculus on the final exam and reported growth in affective domains. Over the three semesters we increased the number of students willing to an IBL course in the future. We will discuss implications of our work and advice for college mathematics instructors who may wish to adopt a similar pedagogical practice.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2020 Fall\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2020 Fall Math Colloquia<\/h2>\n
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September 16<\/b> Virtual, 4:00pm<\/p>\n

Carl Mummert (Marshall University)
\nA case study in computable graph theory: K\u00f6nig’s edge coloring theorem<\/p>\n

Abstract<\/em> Computable graph theory is a subfield of combinatorics and logic. A graph, in this sense, has a set of vertices (points), some of which are connected with edges. Graphs are applied to model many kinds of relationships in numerous disciplines. Computability theory uses a framework originally developed by Alan Turing to study the problems computers are theoretically able to solve. This talk will introduce computable graph theory using a specific theorem. K\u00f6nig’s edge coloring theorem gives a way to assign colors to the edges of a graph using the least number of colors possible. I will introduce the theorem and many results about its computability theoretic properties.<\/p>\n

No prior familiarity with graph theory or computability is needed, and this talk is aimed at a general audience.<\/p>\n

October 21<\/b> Virtual, 4:00pm<\/p>\n

Michael Otunuga (Marshall University)
\nTime Dependent Probability Density Function for Number of Infection in a Stochastic SIS Epidemic Model<\/p>\n

Abstract:<\/em> The closed-form time dependent probability density function of the number of infected individuals at a given time satisfying a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model is derived and analyzed using the Fokker-Planck equation. The mean, median, variance, skewness and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission and recovery rates of the disease. The result is applied using published Covid-19 data\/parameters.<\/p>\n

November 18<\/b> Virtual, 4:00pm<\/p>\n

Michael Schroeder (Marshall University)
\nThe null space of maximum density ASMs<\/p>\n

Abstract:<\/em> At some point in your life, you have been asked to “set it equal to zero and solve.” This is another such time. A large field of research is dedicated to computing the spectrum<\/em> of a matrix, which in part asks the question,<\/p>\n

If A<\/em> is a matrix, for what vectors x<\/strong> does A<\/em> x<\/strong> = 0<\/strong>?<\/p>\n

The set of all solutions to this equation is the null space<\/em> of A<\/em>. In this talk, we look at a particular family of matrices called alternating sign matrices<\/em> (or ASMs for short), which are matrices with only 0s, 1s, and -1s in it that satisfy a certain “alternating” condition.<\/p>\n

We define and describe some properties of maximum density ASMs, then compute their null spaces. Surprisingly, some elementary graph theory was helpful to solve the problem. This research is joint work with Pauline van den Driessche, from the University of Victoria.<\/p>\n

Having some background in linear algebra would be beneficial, but the only requirement is that, at some point in your life, you’ve been asked to set something equal to zero and solve.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2020 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2020 Spring Math Colloquia<\/h2>\n
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February 19<\/b> Smith Hall 516, 4:00pm<\/p>\n

Alaa Elkadry (Marshall University)
\nInference when Data Sources Uncertain<\/p>\n

Abstract:<\/em> Data with uncertain sources are available all around us. Specifically, we\u2019re talking about the cases where each observation has a probability distribution. Randomized response data and assessing possible landing disparity are among the application areas of such data.<\/p>\n

In this talk, examples of some application areas are further discussed, and illustrative examples are provided to demonstrate the calculations for each case discussed.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2019 Fall\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2019 Fall Math Colloquia<\/h2>\n
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September 18<\/b> Smith Hall 516, 4:00pm<\/p>\n

Faith Hensley (Marshall University)
\nExtremal Numbrix Puzzles<\/p>\n

Abstract:<\/em> Numbrix is a puzzle in Parade magazine. The player is given a 9 \u00d7 9 grid with some integers between 1 and 81 filled in. The player then needs to fill in the rest of the integers between 1 and 81 so that consecutive integers appear in adjacent cells of the grid. Generalizing this puzzle we consider m \u00d7 n grids with the entries being the integers between 1 and mn. We say that a set of clues defines a puzzle if there exists a unique solution given those clues. In 2018 Hanson and Nash find the maximum number of clues that fail to define an m \u00d7 n puzzle for all m and n. I present our work on their conjecture concerning the minimum number of clues necessary to define a puzzle. This research is joint work Ashley Peper conducted as part of the 2019 REU program at Grand Valley State University.<\/p>\n

Chloe’ Marcum (Marshall University)
\nExtended Schur Functions<\/p>\n

Abstract:<\/em> The set of quasisymmetric functions homogeneous of degree n form a polynomial
\nvector space, QSym<\/em>, with multiple bases. Many of these bases can be generated
\ncombinatorially using tableaux with various rules. The bases of QSym<\/em> we are interested
\nin are the quasisymmetric Schur functions and the extended Schur functions.
\nBoth generalize the symmetric Schur functions. A common question in linear algebra
\nis how to transition from one basis to another. We have an expansion of
\nextended Schur functions into quasisymmetric Schur functions for a family of indexing
\ncompositions. We prove this expansion combinatorially by using a tree
\nwhose leaves indicate the polynomials that appear in our expansion.<\/p>\n

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October 16<\/b> Smith Hall 516, 4:00pm<\/p>\n

Logan Rose (Marshall University)
\nModeling Malaria with Controls<\/p>\n

Abstract:<\/em> Malaria is a deadly parasitic disease that has been a major threat to public health for centuries, particularly in Sub Saharan Africa and South Asia. Although there are still 200 million cases reported yearly according to the CDC, there have been renewed efforts in recent decades to combat this illness. Mathematicians have created various models using differential equations to simulate the spread of malaria and to determine which control strategies are most effective in reducing the number of new infections. Many of these consider the interactions between humans and the Anopheles mosquito, the primary vector of the disease. This project considers the effectiveness of two popular malaria control strategies: using bed nets and releasing sterile mosquitoes. We used an eight-equation model that combines an SEIR (Susceptible-Exposed-Infected-Recovered) model for the human population, an SEI (Susceptible-Exposed-Infected) model for the vector population, and an additional equation for the sterile mosquito population. In addition, we applied the Next Generation Matrix method to our model to derive a formula for the basic reproduction number for infectious disease. Finally, we apply optimal control theory to find the optimal releasing strategies, and numerical simulations are presented for various cases.<\/p>\n

Michael Waldeck (Marshall University)
\nGeneralizing the Classical Construction for Complete Sets of Mutually Orthogonal Latin Squares<\/p>\n

Abstract:<\/em> Latin squares are a well established topic of study in Mathematics. A Latin square of size n is an n by n square where each number from 1 to n appears exactly once in each row and in each
\ncolumn. Two Latin squares are orthogonal mates if, when the squares are superimposed, every
\npossible ordered pair of entries appears in the superimposed square. In the 18th century, Leonhard
\nEuler studied the question of finding a complete set of mutually orthogonal Latin squares (MOLS)
\nof a given size. Euler proved that for each n, a set of n by n MOLS can have no more than n – 1
\nsquares. It has also been proved that, where n is a prime power, this upper bound is achieved
\nthrough the classical construction. The classical construction for a complete set of MOLS of size
\nn by n can be given by a formula M(i, j) = i + cj, where c is a nonzero element in the finite field of order n. We study the number of orthogonal mates and the graph of the mate relationship between a family of Latin squares based on a generalization of that formula. That is, when q is prime, we study the set of Latin squares of size q by q that can be given by a formula S(s, c)(i, j) = s(i) + cj,
\nwhere s mapping the finite field of order q to itself is a permutation of the field, c is a nonzero element in the finite field of order q, and the addition and multiplication are carried out in the finite field.<\/p>\n

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November 20 <\/b> Smith Hall 530, 4:00pm<\/p>\n

Carl Mummert (Marshall University)
\nHow to Multiply Big Natural Numbers<\/p>\n

Abstract:<\/em> Big natural numbers are all around. They keep your data private on the internet, and scientists use them for high precision simulations. Adding big numbers is not very hard, but multiplying them is much more challenging. The problem of multiplying numbers efficiently is at the border between mathematics and computer science.<\/p>\n

I will introduce several multiplication algorithms currently used in state of the art software. Then I will describe a breakthrough announced by two researchers in March 2019. They produced an algorithm that can multiply two natural numbers – of any size – with an efficiency we think is optimal. This talk is aimed at anyone with a background of college algebra or higher.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2019 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2019 Spring Math Colloquia<\/h2>\n
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March 20<\/b>
\nJiyoon Jung (Marshall University)
\nEnumeration of Fuss-Schroder paths by types and connected components
\nSmith Hall 516, 4:00pm<\/p>\n

Abstract:<\/em>\u00a0Catalan numbers form a sequence of natural numbers that occur in various important counting problems in Combinatorics. Dyck paths are one of the problems that engaged Catalan numbers. In this talk, the applications of Dyck paths are introduced by considering types of paths, connected blocks, Schroder paths, and Fuss analogues.<\/p>\n

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April 17<\/b>
\nMichael Schroeder (Marshall University)
\nPutting Numbers in Grids: Theory and Applications
\nSmith Hall 516, 4:00pm<\/p>\n

Abstract:<\/em>\u00a0There are many games that involve putting numbers in a grid, like Sudoku, but there are equally many theoretical and practical applications for putting numbers in a grid. Grids with certain conditions met, like no numbers repeated in a row or column, have uses in cryptography, statistics, and experimental testing.<\/p>\n

In this talk, we begin with an introduction to Latin squares (a grid of numbers meeting certain Sudoku-like conditions) and discuss a few of their many applications. We then look at some embedding problems (completely filling a partially filled grid with certain conditions) and discuss some recently published results in this area.<\/p>\n

You may not improve your Sudoku-solving skills by attending this talk, but you should gain some appreciation for why such games can be useful in the real world!<\/p>\n

This is a talk for a general audience! Tell your friends!<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

\n 2018 Fall\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2018 Fall Math Colloquia<\/h2>\n
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September 19<\/b>
\nElizabeth Niese (Marshall University)
\nThe RSK algorithm and applications
\nSmith Hall 516, 4:00pm<\/p>\n

Abstract:<\/em>\u00a0 The Robinson-Schensted-Knuth (RSK) algorithm is a classical algorithm in algebraic combinatorics. It is a bijection between words and pairs of tableaux which has many interesting combinatorial properties. There are a number of distinct constructions equivalent to this algorithm, including the jeu-de-taquin and Viennot’s shadow lines construction. We will look at several of these constructions and their use in proofs of algebraic formulas.<\/p>\n

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October 17<\/b>
\nChlo\u00e9 Marcum (Marshall University)
\nUsing polynomials to study knots
\nSmith Hall 516, 4:00pm<\/p>\n

Abstract:<\/em>\u00a0 A knot is any closed loop in space. Two knots may be the same knot even though they appear to be different. A local move is a change to a small portion of a knot and the rest of the knot is assumed to stay the same. A local move may or may not change the knot. An invariant is a characteristic of a knot that help us tell the difference between knots. In our research, we studied certain polynomials that are knot invariants. We studied the effect of certain local moves on Homflypt and Kauffman polynomials. As a consequence, we discovered some new properties of these invariants.<\/p>\n

This research was completed in summer 2018 as part of a Research Experience for Undergraduates (REU) at St Mary\u2019s College of Maryland. At the end of the talk, I will share general information about REUs as well as my experience at St. Mary\u2019s.<\/p>\n

Knot theory is an area of math that is understandable without a lot of math background. All students interested in math are encouraged to attend.<\/p>\n

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November 28<\/b>
\nRaid Al-Aqtash (Marshall University)
\nMarket Basket Analysis
\nSmith Hall 516, 4:00pm<\/p>\n

Abstract:\u00a0 <\/em>Market basket analysis is a data mining technique based upon using association rules to uncover the purchasing trends in large transaction datasets. The key factor here is to determine possible lists of items that are frequently sold together. In this talk, I will speak about association rules and how they can be used by large retail companies in market basket analysis. A real dataset will be provided in an application of association rules.<\/p>\n

Keywords and phrases: data mining, basket analysis, beer and diapers, association rules, support, confidence, lift.<\/em><\/p>\n

This will be a general audience talk, using a bit of information about proportions and percentages.<\/p>\n

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\n 2018 Spring\n <\/div>\n\n \n \n <\/path>\n <\/svg>\n <\/span>\n <\/button>\n\n \n
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2018 Spring Math Colloquia<\/h2>\n
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February 21<\/b>
\nMichael Otunuga (Marshall University)
\nGlobal stability for a (2n+1)-dimensional HIV\/AIDS epidemic model with treatments
\nSmith Hall 518, 4:00pm<\/p>\n

Abstract:<\/em> In this work, we derive and analyze a (2n+1)-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treatment strategy of regular HIV testing and immediate treatment with Antiretroviral Therapy (ART) is investigated in the presence and absence of noise. By defining R(0,n), R(t,n) and R<\/strong>(t,n) as the deterministic basic reproduction number in the absence of ART treatments, deterministic basic reproduction number in the presence of ART treatments and stochastic reproduction number in the presence of ART treatment, respectively, we discuss the stability of the infection-free and endemic equilibrium in the presence and absence of treatments by first deriving the closed form expression for R(0,n), R(t,n) and R<\/strong>(t,n). We show that there is enough treatment to avoid persistence of infection in the endemic equilibrium state if R(t,n)=1. We further show by studying the effect of noise in the transmission rate of the disease that transient epidemic invasion can still occur even if R(t,n)<1. This happens due to the presence of noise (with high intensity) in the transmission rate, causing R<\/strong>(t,n)>1. A threshold criterion for epidemic invasion in the presence and absence of noise is derived. Numerical simulation is presented for validation.<\/p>\n

\n

April 19<\/b>
\nCarl Mummert (Marshall University)
\nThe number TREE(3), and counting down in base infinity
\nSmith Hall 518, 4:00pm<\/p>\n

Abstract:<\/em>\u00a0 The motivation of this talk is a peculiar situation from computer science. In some cases, we know that a program will eventually stop, but we have no way to concretely describe or even bound the number of steps the program will take. For one such program, the number of steps is a number TREE(3) so large that there is no concrete way to describe it or bound it from above.<\/p>\n

This talk will introduce TREE(3) and the related result known as Kruskal’s theorem. We will look at some simpler versions of the theorem, leading us to a “base infinity” number system. This system is like base ten, but each digit can be arbitrarily large. We will see that counting down to 1 from a base infinity number is not as easy as it sounds.<\/p>\n

The work on base infinity numbers is joint research with mathematics major Samantha Colbert.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

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2017 Fall Math Colloquia<\/h2>\n
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September 20<\/b>
\nMatt Davis (Muskingum University)
\nNon-transitive dice: Constructions, Complications, and Questions
\nSmith Hall 509, 4:00pm<\/p>\n

Abstract:<\/em> Non-transitive dice have been a source of fascination for mathematicians for over 50 years. We are given a set of dice which are numbered in strange ways. Each player chooses a die, rolls it, and the higher roll wins. Our intuition suggests that in any set of dice, one is the “best”. However, it turns out that it is relatively easy to construct a set of dice which are non-transitive – where most dice are strong against some opponents and weak against others. In this talk we will look at lots of examples of these fascinating objects, aiming for a goal of a single construction that allows us to create a set of dice in any desired configuration. We will also talk briefly about the much harder problem of finding the most efficient way to create such a set of dice.<\/p>\n

\n

October 18<\/b>
\nSkye Smith (Service Pump & Supply, Huntington WV)
\nThree Things I Wish I Had Known When I Was a Math Major
\nSmith Hall 509, 4:00pm<\/p>\n

Abstract:<\/em> Since graduating from Marshall University with an applied mathematics degree in 2014, I have used my degree in several various business roles. Each position has provided a new way to use my mathematics degree in a business setting and each role brought new lessons I wished I had considered throughout my time as an undergraduate student. In this presentation, I will discuss the three things I wish I had known while I was a mathematics major at Marshall University. Addressing these three observations will help guide mathematics students who are hoping to use their skill set in a business setting at a time when math minds are more important than ever to companies undergoing digital transformations and embracing the era of big data.<\/p>\n

\n

November 15<\/b>
\nAvishek Mallick (Marshall University)
\nStatistical Modeling of Discrete\/Count Data<\/p>\n

Abstract:<\/em> In this talk, I will introduce the idea of Statistical modeling, especially in context of count data. We will look at different facets of data fitting like estimation techniques and criterion for assessing goodness-of-fit. A substantial part of the talk will be about modeling inflated count data. We will be looking at lots of real world examples. This talk is intended for a general audience and thus should be appropriate for Mathematics undergraduate and graduate students.<\/p>\n\n\n <\/div>\n <\/div>\n <\/div>\n \n \n \n

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2017 Spring Math Colloquia<\/h2>\n
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January 16<\/strong>
\nCarl Mummert (Marshall University)
\nMathematical Induction: Through Infinity and Beyond<\/p>\n

\n

February 16<\/strong>
\nJohn Asplund (Dalton State University)
\nVertex Colouring Degeneracy and the Limits of Edge-Colouring Techniques<\/p>\n

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2016 Fall Math Colloquia<\/h2>\n
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September 21<\/strong>
\nMichael Schroeder (Marshall University)
\nA Survey of Graph Decompositions<\/p>\n

\n

October 24<\/strong>
\nElizabeth Niese (Marshall University)
\nThe combinatorics of symmetric polynomials<\/p>\n

\n

November 16<\/strong>
\nScott Sarra (Marshall University)
\nRadial Basis Functions Methods and their Implementation<\/p>\n

\n

November 30<\/strong>
\nJiYoon Jung (Marshall University)<\/p>\n

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2016 Spring Math Colloquia<\/h2>\n
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January 26<\/strong>
\nAvishek Mallick (Marshall University)
\nA Look at Permuatation (a.k.a. Randomization) Tests<\/p>\n

Abstract:<\/em> Most of the standard statistical hypothesis testing procedures are based on the normality assumption, i.e., the data is normally distributed and also on few other assumptions. What happens if these assumptions do not hold? The answer lies in the Permutation testing approach also known as randomization or re-randomization tests. In this talk, I will discuss the randomization principle and also how these tests are impervious to complications that defeat other classical statistical significance testing techniques.<\/p>\n

Keywords:<\/em> Permutation testing, Statistical significance, Randomization, Distribution-free approach, P-values.<\/p>\n

\n

February 24<\/strong>
\nCarl Mummert (Marshall University)
\nIncompleteness in mathematics<\/p>\n

Abstract:<\/em> In 1931, Kurt G\u00f6del published two theorems, known as the \u201cincompleteness theorems,\u201d which revolutionized the foundations of mathematics in much the same way that Einstein\u2019s theory of relativity revolutionized the foundations of physics. In this talk, I will discuss what the incompleteness theorems say in plain language, and why they were so revolutionary. Along the way, we will encounter a few other few other major figures from the foundations of mathematics: Bertrand Russell, David Hilbert, Hermann Weyl, and L.E.J. Brouwer. No mathematical background beyond College Algebra is required for this talk.<\/p>\n

\n

March 7<\/strong>
\nShubhabrata Mukherjee (University of Washington, Seattle)
\nGenetic analyses of late-onset Alzheimer\u2019s Disease<\/p>\n

Abstract:<\/em> Genetic epidemiology holds great potential for personalized medicine and improved biological knowledge of disease pathogenesis. In this talk, I will introduce some basic concepts needed to understand, analyze, and interpret Genome-wide Association Studies (GWAS) data with late-onset Alzheimer\u2019s disease (LOAD) as an example. I will briefly talk about extending these results to gene-wide and network\/pathway-based analysis, which are complementary to GWASs.<\/p>\n

\n

March 8<\/strong>
\nShubhabrata Mukherjee (University of Washington, Seattle)
\nIntroduction to Genetic Epidemiology in GWAS era<\/p>\n

Abstract:<\/em> Alzheimer\u2019s disease is the most common form of dementia. Genetics of late-onset Alzheimer\u2019s disease (LOAD) is very complex. Genome-wide Association Studies (GWAS) are an important first step. Gene-based and network\/pathways based analyses also contribute to the understanding of genetic determinants of LOAD. Thus, a three-component approach \u2014 GWAS, gene-based, and network-based analyses \u2014 is likely to best illuminate genetic determinants of a disease. I will explore the three component approach in this talk.<\/p>\n

\n

April 6
\nAnna Mummert (Marshall University)<\/p>\n

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2015 Fall Math Colloquia<\/h2>\n
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September 2<\/strong>
\nMichael Schroeder (Marshall University)
\nTournaments: Scheduling Them Fairly and More!<\/p>\n

Abstract:<\/em> In this talk, we will discuss round-robin tournaments \u2014 tournaments in which each team plays every other team. We’ll look at how to schedule games in a way so that, if there is only one playing surface, that no team is unreasonably burdened by playing games back-to-back. We’ll also talk about what the possible win-loss records are for teams which play in a round-robin tournament. We’ll relate this to complete graphs, score sequences, Landau’s inequalities, and matching sequencibility. A majority of this talk will be accessible to a general audience.<\/p>\n

\n

September 28<\/strong>
\nNick Loehr (Virginia Tech)
\nRook Theory 101<\/p>\n

Abstract:<\/em> Combinatorics is the mathematical theory of counting. In this talk, we introduce combinatorics through the subject of rook theory \u2014 which has nothing to do with chess! The first goal of rook theory is to count configurations of rooks on generalized chessboards so that no two rooks attack each other. The k\u2019th rook number of a board counts the number of such ways to place k rooks on the board. It often happens that two different boards share the same rook numbers. This talk investigates when and why this occurs by using geometric and algebraic manipulations of boards and rook placements. We present theorems of Foata\/Schutzenberger and Goldman\/Joichi\/White characterizing rook-equivalent boards in various ways. The techniques used illustrate three branches of modern combinatorics \u2014 enumerative combinatorics, bijective combinatorics, and algebraic combinatorics. No prior knowledge of counting (or chess) is required for this talk.<\/p>\n

\n

September 29<\/strong>
\nNick Loehr (Virginia Tech)
\nSweep Maps and Bounce Paths<\/p>\n

Abstract:<\/em> Mathematics is filled with open (unsolved) problems, ranging from deep foundational issues of physics, computation, geometry, and number theory to highly specialized research questions. This talk describes an open problem in algebraic combinatorics that can be stated and investigated with virtually no mathematical background, although the problem appears to be fiendishly challenging to solve. We define a family of maps on words, called \u201csweep maps.\u201d A sweep map assigns a level to each letter in a word according to a simple rule, then sorts the letters according to their level. Surprisingly, although sweep maps act by sorting, they appear to be invertible: i.e., different input words are always sent to different output words by any given sweep map. The open problem is to prove the invertibility of all sweep maps, preferably by explicitly describing the inverse functions. We explain some known special cases of this problem using a model in which words are visualized using lattice paths. In some cases, we can pass from a lattice path to an associated \u201cbounce path,\u201d which provides the additional data needed to invert the sweep map. These bounce paths originally arose in the study of objects called q,t-Catalan polynomials. Many algorithms that have appeared in the q,t-Catalan literature over the last 20 years turn out to be particular instances of the sweep maps or their inverses. The sweep maps thus provide a simple unifying framework for understanding all of these algorithms.<\/p>\n

\n

October 21<\/strong>
\nMichael Otunuga (Marshall University)
\nStochastic Modeling of Energy Commodity Spot Price Processes<\/p>\n

Abstract:<\/em> In this work, we undertake the study to shed light on world oil market and price movement, price balancing process and energy commodity behavior. We initiate the development of a stochastic model of energy commodity pricing. A system of stochastic model for dynamic of energy pricing process is proposed. Different methods for parameter estimation is discussed. In addition, by developing a Local Lagged Adapted Generalized Method of Moment (LLGMM) method, an attempt is made to compare the simulated estimates derived using LLGMM and other existing method. These developed results are applied to the Henry Hub natural gas, crude oil, coal and ethanol data sets.<\/p>\n

\n

November 4<\/strong>
\nMartha Yip (University of Kentucky)
\nColoring: the Algebraic Way<\/p>\n

Abstract: <\/em>Suppose we want to color the countries on a map so that if two countries share a border, then they must be assigned different colors. What is the smallest number of colors that will do the job? The answer is the famous Four Color Theorem, which states that any map can be colored by at most four colors. Inspired by this problem, Birkhoff introduced the chromatic polynomial to study colorings of a graph. In this talk, we discuss some recent developments in the study of the chromatic polynomial; from a multivariable generalization known as the chromatic symmetric function, to a homology theory whose Euler characteristic recovers the chromatic symmetric function. No prior knowledge of any of the above terminology is assumed.<\/p>\n

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2015 Spring Math Colloquia<\/h2>\n
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February 4<\/strong>
\nElizabeth Niese (Marshall University)
\nWhat do trigonometry and combinatorics have to do with each other?<\/p>\n

Abstract:<\/em> Combinatorics is the study of how to count. Results from the field of combinatorics are used in probability and statistics, computer science, physics, and elsewhere. Trigonometry is the study of triangles and how their angles relate to side lengths. At first glance, these two topics seem quite unrelated. In this talk we will look at how some common trigonometric functions encode the number of up-down permutations.<\/p>\n

\n

February 17<\/strong>
\nDavid Cusick (Marshall University)
\n350 Years of Service … and Then Pffft!<\/p>\n

Abstract:<\/em> After more than three centuries as a well-known calculation tool, the slide rule was eclipsed by electronic calculators in the 1970s. Based on the \u201ccommon\u201d (base 10) logarithm, this analog device was state-of-the-art before its popularity collapsed. The elementary slide rule aided the approximation of products, quotients, powers and roots. A variety of other models could handle more sophisticated functions. Some rules are still in regular use even at the present time. Virtual rules exist, and there are some \u201capps\u201d for that. This talk will just touch the basic theory and a few examples. Logarithm laws are well represented. If time permits, we can see a photo gallery. Everything should be readily accessible to those who are at and above pre-calculus.<\/p>\n

\n

March 4<\/strong>
\nGregory Moses (Ohio University)
\nClustering and Stability of Cyclic Solutions in the Cell Division Cycle of Yeast<\/p>\n

Abstract:<\/em> It has long been observed that in a large, well-mixed yeast culture (i.e. a bioreactor), yeast autonomous oscillations (such as dissolved oxygen percentages) are correlated with bud index, but only recently have researchers (biological or mathematical) attempted to analyze the cause of this correlation. They proposed a signaling model whereby a concentration of cells in one part of the cell division cycle might influence cells in other parts of the cycle through diffusible chemical products. We briefly introduce the model, then present an overview of work we have done analyzing the existence, stability and instability of periodic orbits under varying types of feedback. This is joint work with Nathan Breitsch.<\/p>\n

\n

March 27\u201328<\/strong>
\nMAA Ohio Section Meeting at Marshall University<\/p>\n

\n

April 14<\/strong>
\nJudy Day (University of Tennessee)
\nModeling the host response to inhalation anthrax to uncover the mechanisms driving risk of disease.<\/p>\n

Abstract:<\/em> Bacillus anthracis, the causative agent of anthrax, can exist in the form of highly robust spores, making it a potential bio-terror threat. Once inhaled, the spores can germinate into vegetative bacteria capable of quick replication, leading to progressive disease and death. There is a critical need to better quantify the risk of disease from different inhalation exposure scenarios. Key to this effort is the use of mathematical and computational modeling to uncover the mechanisms driving risk. To this end, this presentation will discuss ongoing work on the development of models and methods that explore the host response to inhalation anthrax and provide insight into the mechanisms that drive the risk of disease. This is joint work is joint University of Tennessee graduate student Buddhi Pantha, and the NIMBioS Working Group on Modeling Anthrax Exposure.<\/p>\n

\n

April 15<\/strong>
\nJudy Day (University of Tennessee)
\nDetermining the what, when, and how of therapeutic intervention strategies for controlling complex immune responses.<\/p>\n

Abstract:<\/em> Ideally, when challenged with a bacterial insult, a host orchestrates an immune response that, not only eliminates the offending pathogen, but also restores the host to homeostasis. However, due to the complex nature of the response, this is not always possible, especially in critically ill patients. Clearly, intervention is needed; however, determining the types of intervention that should be given, when they should be given, and in what amount remains a challenge. Computational modelling and control methodologies can provide fresh insight into this challenging biomedical problem and potentially offer techniques to answer these difficult questions. This talk will discuss computational control methodologies that are being explored to determine the what, when, and how of therapeutic intervention strategies for controlling complex immune responses.<\/p>\n

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2014 Fall Math Colloquia<\/h2>\n
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September 3<\/strong>
\nCarl Mummert (Marshall University)
\nIs that a Prime Number?<\/p>\n

Abstract:<\/em> How can you tell whether a number is prime? Is 920,419,823 prime? I will talk about several methods for testing whether a number is prime, including the groundbreaking AKS algorithm published by Agrawal, Kayal, and Saxena in 2002, which was the first efficient general-purpose test for primes. Along the way we will see several topics from discrete mathematics that don\u2019t seem very related to primes at first glance, such as polynomials and modular arithmetic. I will also talk about the history of the three Indian computer scientists behind the AKS algorithm.<\/p>\n

\n

September 17<\/strong>
\nLaura Adkins (Marshall University)
\nInteractive Regression Models with Centering<\/p>\n

Abstract:<\/em> Including interaction in a multiple regression model can increase its accuracy. Unfortunately, it also leads to multicollinearity, which violates the requirements of linear regression. I will discuss the use of centering to resolve this problem. I will then use an applied example to illustrate its use and explore its effectiveness.<\/p>\n

\n

October 1<\/strong>
\nMichael Schroeder (Marshall University)
\nLatin squares and their completions<\/p>\n

Abstract
\nIf you\u2019ve even finished a Sudoku puzzle, then you\u2019ve seen a \u201ccompleted\u201d Latin square. A Latin square is an array of symbols where each symbol appears exactly once in each row and each column. A solution to a Sudoku puzzle is a Latin square, with the additional constraint of having no repeated symbol in each $3\\times 3$ block. Although Sudoku has only been popular for the past decade, mathematicians have been studying Latin squares since the 18th century, and have many applications including coding theory and experimental design. We will begin by discussing a brief exposition of Latin squares. Then we will go over some properties of Latin squares and some classical results identifying when partial Latin squares can be completed. To finish, we will talk about some recent results in the field. The beginning of the talk should be very accessible, and toward the end there will be some technical discussion.<\/p>\n

\n

October 15<\/strong>
\nXue Gong (Ohio University)
\nClustering and Noise-Induced Dispersion in Cell Cycle Dynamics (No Link to Abstract)<\/p>\n

\n

November 5<\/strong>
\nRichard Brualdi (University of Wisconsin\u2013Madison)
\nThe Gale-Berlekamp Light-Switching Problem and a Permutation Variation<\/p>\n

Abstract:<\/em> Consider an n by n array of light bulbs each controlled by a switch. Suppose there are also 2n other switches which allow one to simultaneously switch all the light bulbs in a row or all the light bulbs in a column. Now use the individual switches and turn some of the light bulbs on. With the row and column switches only, can one get all the lights in the off position? If not, how few on-lights are possible? This problem, its connections to coding theory, and a permutation variation is the subject of this talk.<\/p>\n

\n

November 6<\/strong>
\nRichard Brualdi (University of Wisconsin\u2013Madison)
\nAll Things Bruhat: Matrix Bruhat Decomposition, Complete Flags, Bruhat Order of Permutations, (0,1) and Integral Matrices, and Tournaments<\/p>\n

Abstract:<\/em> The title is a bit of an exaggeration, but we will discuss the topics it contains and various connections between them.<\/p>\n

\n

November 19<\/strong>
\nBismark Oduro (Ohio University)
\nDesigning Optimal Spraying Strategies for Controlling Re-infestation by Chagas Vectors<\/p>\n

Abstract:<\/em> Chagas disease is a major health problem in rural South and Central America where an estimated 8 to 11 million people are infected. It is a vector-borne disease caused by the parasite Trypanosoma cruzi, which is transmitted to humans mainly through the bite of insect vectors from several species of so-called \u201ckissing bugs.\u201d One of the control measures to reduce the spread of the disease is insecticide spraying of houses to prevent infestation by the vectors. However, re-infestation of homes by vectors has been shown to occur as early as four to six months after insecticide-based control interventions. In this talk, I will present re-infestation models that shed light on the effectiveness of the insecticide spraying. In particular, I will present both numerical explorations and some mathematical results. Comparison of the effectiveness of two spraying strategies namely; continuous and intermittent shows no statistically significant difference between the two strategies for small population size. For large population size, intermittent treatment is slightly more effective than continuous treatment. Another interesting result is the existence of a hysteresis-like phenomenon. This occurs when two different spraying rates lead to two different numbers of infested units at equilibrium. These results have potentially important implications for designing cost-effective control spraying strategies.<\/p>\n

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2014 Spring Math Colloquia<\/h2>\n
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March 10<\/strong>
\nJeffry L. Hirst (Appalachian State University)
\nAlan and Ada’s Theoretical Machines<\/p>\n

Abstract:<\/em> Ada Lovelace is often called \u201cthe first computer programmer,\u201d though she died a century before the first general purpose computers were built. This claim is based on the notes she appended to her translation of Menabrea\u2019s 1842 paper, Notions sur la Machine Analytique de M. Charles Babbage. Alan Turing is often called \u201cthe father of theoretical computer science\u201d on the basis of his 1936 article On computable numbers, with an application to the Entscheidungsproblem. Lovelace\u2019s notes describe Babbage\u2019s Difference Engine and Babbage\u2019s Analytical Engine, and Turing\u2019s paper proves the existence of a Universal Turing Machine. This talk will compare the designs and capabilities of these early theoretical computing machines.<\/p>\n

\n

March 11<\/strong>
\nJeffry L. Hirst (Appalachian State University)
\nReverse Mathematics, Graphs, and Matchings<\/p>\n

Abstract:<\/em> How can we tell if two theorems are essentially the same? If we can prove that they are equivalent, then they are in some sense interchangeable. If our equivalence proof relies on a particularly small set of assumptions, then our claim of similarity is even stronger. This is the fundamental motivation of reverse mathematics, a program in the foundations of mathematics initiated by Harvey Friedman and Stephen Simpson. This talk will illustrate some results and techniques of the program.<\/p>\n

\n

April 9<\/strong>
\nJiYoon Jung (Marshall University)
\nThe topology of chain selected complexes of a poset PDF<\/p>\n

Abstract:<\/em> For each composition ~c we show that the order complex of the poset of pointed set partitions \u03a0\u2022 ~c is a wedge of \u03b2(~c) spheres of the same dimensions, where \u03b2(~c) is the number of permutations with descent composition ~c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module SB where B is a border strip associated to the composition ~c. We also study the filter of pointed set partitions generated by knapsack integer partitions and show the analogous results on homotopy type and action on the top homology.
\nLet \u039b be a sub semi-group of the natural numbers N. I am interested in filters of the partition lattice consisting of partitions where every block size belongs to \u039b. Since \u039b is closed under addition, these collections of partitions do form a filter in the partition lattice. In the case that \u039b is generated by \u3008a, d\u3009 where a and d are relatively prime, I conjecture that the action of the symmetric group on the top homology group of the associated order complexes is a direct sum of Specht modules. Precisely, I conjecture that \u02dcHk(\u2206) is isomorphic to the direct sum of Specht modules \u2295~c S\u03b2(~c) where ~c = (c1, c2, . . . , ck+2) ranges over all compositions of n satisfying ci = a + mi \u00b7 d for 0 \u2264 mi < a.
\nThis is joint work with Richard Ehrenborg.<\/p>\n

\n

April 11<\/strong>
\nLingxing Yao (Case Western Reserve University)
\nMathematical Modeling and Simulation for Biological Applications<\/p>\n

Abstract:<\/em> In this talk, I will go over some of my research projects in mathematical modeling and simulation for biological applications. I will focus on the analysis of a Hydrogel\/Enzyme drug delivery oscillator, which involved mathematical modeling and dynamical analysis of models. It is well known that hydrogels are soft materials similar to natural tissue, and can be found in applications such as food additives, contact lens, cosmetic surgery, wound healing, and drug delivery devices. Since hydrogels are made of cross linked polymer networks that are capable of absorbing large amounts of water, they can be present in swollen or collapsed state. Under carefully designed physical and chemical conditions, we could observe volume phase transitions in polyelectrolyte hydrogels between those states, sometimes repeatedly. In this presentation, I will address the modeling of gel swelling, by combining the theory of the elastic, electrostatic and mixing energy in a model membrane made of polyelectrolyte hydrogel. Based on these energy principles, it is possible to propose the mathematical model system which is capable of explaining the oscillatory volume phase transition seen in a real membrane oscillator built in engineering laboratory for the purpose of hormone drug delivery. Some detailed analysis and results of the model system will be presented.<\/p>\n

\n

April 14<\/strong>
\nStephen Flood (University of Connecticut \u2013 Waterbury)
\nPath, trees, and the computational strength of a packed Ramsey’s theorem<\/p>\n

Abstract:<\/em> Ramsey theory is a branch of combinatorics which provides results like the following: any large enough graph must either contain a large complete subgraph (all vertices connected) or a large independent set (no vertices connected). In this talk, we will introduce a \u00e2\u20ac\u0153packed\u201d version of Ramsey\u2019s theorem, due to Erdos and Galvin, which combines aspects of finite and infinite Ramsey theory. We will discuss the techniques used to extract these packed homogeneous sets, and we will study their strength using the tools of computability theory and reverse mathematics.<\/p>\n

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2013 Fall Math Colloquia<\/h2>\n
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October 2<\/strong>
\nLynne Yengulalp (University of Dayton)
\nTopological completeness<\/p>\n

Abstract:<\/em> I will start by reviewing the Baire Category Theorem for complete metric spaces. I will then talk about other classes of topological spaces for which the Baire Category Theorem holds. Such spaces have \u201cgeneralized\u201d completeness properties extending from the familiar local compactness property to the relatively new property of domain representability.<\/p>\n

\n

October 30<\/strong>
\nRoger Estep (Marshall University)
\nFiltered leapfrog time integration with enhanced stability properties<\/p>\n

Abstract:<\/em> The Leapfrog method for the solution of Ordinary Differential Equation initial value has been historically popular for several reasons. The method has second order accuracy, requires only one function evaluation per time step, and is non-dissipative. Despite the mentioned attractive properties, the method has some unfavorable stability properties. The absolute stability region of the method is only an interval located on the imaginary axis rather than a region in the complex plane. The method is only weakly stable and thus exhibits computational instability in long time integrations over intervals of finite length. In this work the use of filters is examined for the purposes of both controlling the weak instability and also enlarging the size of the absolute stability region of the method.<\/p>\n

Robert Hughes (Marshall)
\nAgent-based modeling of pandemic influenza<\/p>\n

Abstract:<\/em> A striking characteristic of influenza pandemics is the multiple peaks of infection. For example, the United States has experienced two peaks of infection in each of the past four influenza pandemics, one peak during the summer months and a second peak during the typical flu season. In contrast, the number of infected individuals peaks only once during a seasonal flu. The mechanisms that cause the multiple peaks of infection during pandemic influenza seasons are not well understood. The goal of this project is to use agent-based modeling to investigate mechanisms that can generate two peaks of infection.
\nIn this talk I will describe the susceptible-exposed-infectious-recovered (SEIR) agent-based model developed in Netlogo for simulating the 2009 H1N1 influenza pandemic. The incubation and infectiousness periods are drawn from gamma distributions. The model is calibrated by matching known average daily contacts and key epidemiological quantities, such as the basic reproduction number, the number of new infections generated from one infectious person at the beginning of the outbreak. Also, I will discuss the results of model simulations that include waning immunity, which is one potential mechanism for generating multiple peaks of infection.<\/p>\n

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November 18<\/strong>
\nThomas Mathew (University of Maryland-Baltimore County)
\nThe Assessment of Bioequivalence: A Statistical Overview<\/p>\n

Abstract:<\/em> The topic of bioequivalence deals with procedures for testing the equivalence of two drug products: typically, a generic drug and a brand name drug on the market. Bioequivalence testing consists of showing that the concentration of the active drug ingredient that enters the blood is similar for the two drugs. Area under the time-concentration curve, or the AUC, is usually used for this purpose, and the data are obtained based on cross-over designs. In the talk, the bioequivalence problem will be introduced, its history will be discussed, and examples will be provided. Statistical criteria that are used for bioequivalence testing, especially the criterion of average bioequivalence, will be discussed. Methodology for testing the hypotheses of average bioequivalence will be addressed. The emerging area of equivalence testing in the context of biosimilars will be briefly touched upon.<\/p>\n

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November 19<\/strong>
\nThomas Mathew (University of Maryland-Baltimore County)
\nMethodology and Some Applications<\/p>\n

Abstract:<\/em> Standard likelihood based methods that are usually used to analyze data arising from a parametric model are typically accurate to the first order. Higher order inference procedures provide major improvements in accuracy, and are available for discrete as well as for continuous data. In the talk, two applications of higher order inference will be described. Both the applications deal with the computation of an upper tolerance limit: a limit that is expected to capture a specified proportion or more of a population with a given confidence level. The limit is constructed using a random sample, and the confidence level refers to the resulting sampling variability.
\nThe first application that will be discussed is on the computation of tolerance limits under the logistic regression model for binary data. The data consist of binary responses, and upper tolerance limits are to be constructed for the number of positive responses in future trials corresponding to a fixed level of the covariates. The problem has been motivated by an application of interest to the U.S. Army, dealing with the testing of ballistic armor plates for protecting soldiers from projectiles and shrapnel, where the probability of penetration of the armor plate depends on covariates such as the projectile velocity, size of the armor plate, etc. The second application is on the computation of upper tolerance limits under a general mixed effects model with balanced or unbalanced data. Higher order inference procedures will be used to obtain accurate solutions in both the applications. Numerical results, examples and data analysis will also be reported.<\/p>\n

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January 30<\/strong>
\nElizabeth Niese (Marshall)
\nA family of Catalan objects<\/p>\n

Abstract:<\/em> The Catalan numbers appear in many surprising places with over 200 known classes of objects counted by the Catalan numbers. Many of the objects counted by the Catalan numbers have connections to other areas of mathematics, such as algebra and geometry, and even to computer science. In this talk we will look at a particular class of objects, how they can be counted elegantly, and some of the connections between these objects and algebra.<\/p>\n

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February 20<\/strong>
\nAnna Mummert (Marshall)
\nUnit costs in optimal control of epidemics<\/p>\n

Abstract:<\/em> The cost of vaccinating an individual during an epidemic is not constant. It is assume that it is cheaper to vaccinate the first individuals and more expensive to vaccinate the last few individuals, due to logistics. In this talk, I will use mathematical modeling to compare the effects of different unit cost functions on the epidemic. I will describe a susceptible-exposed-infected-removed (SEIR) model of an epidemic, where susceptible individuals can be vaccinated and removed from the epidemic. Given a particular unit cost function for the vaccination, it is possible to determine the optimal vaccination rate that minimizes an associated \u201ctotal cost\u201d function, using the technique known as Pontryagin\u2019s maximum principle. Different unit cost functions result in different optimal vaccination rates. Pontryagin\u2019s maximum principle will be explained and several unit cost functions will be considered.<\/p>\n

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April 24<\/strong>
\nCarl Mummert (Marshall)
\nIf 1+1=9, does 2+2=7?<\/p>\n

Abstract:<\/em> In mathematics, we often look at \u201cif\/then\u201d relationships. It turns out there are several ways to interpret deceptively simple questions such as \u201cIf 1 + 1 = 9, does 2 + 2 = 7?\u201d, which lead to surprising answers. I will explain how techniques of mathematical logic help us understand these questions and talk about recent undergraduate and graduate student research at Marshall in this area. This talk is aimed at undergraduates. Students who are taking algebra and calculus classes are particularly invited to attend.<\/p>\n

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2012 Fall Math Colloquia<\/h2>\n
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October 3<\/strong>
\nJohn Drost (Marshall)
\nWhat is Strategic Voting and What Can Be Done About It?<\/p>\n

Abstract:<\/em> In any election with three or more candidates there are many different schemes for choosing a winner. We will look at a couple of them, the \u2018instant-runoff\u2019 procedure and the Borda count. Also, these schemes are vulnerable to \u2018strategic voting\u2019; the idea that by changing their votes from their real preferences, some voter or voters can obtain a more favorable outcome.<\/p>\n

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2012 Spring Math Colloquia<\/h2>\n
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January 25<\/strong>
\nMichael Schroeder (Marshall)
\nCyclic Matching Sequencibility of Graphs<\/p>\n

Abstract:<\/em> Suppose you have 7 basketball teams in a round-robin tournament (each pair of teams play a game) and only one court. How can you schedule the games \u201cfairly\u201d for everyone? \u201cFair\u201d is a vague term; when we say fair, we want all teams to have a maximal amount of down time between successive games (so no team plays two games in a row, for example). The answer to this question can be found using matching sequencibility.<\/p>\n

Let G be a graph with m edges. Order the edges of G with the labels 1,2,\u2026,m. The matching number of this ordering is the largest number d such that each consecutive d edges form a matching (don\u2019t touch). The matching sequencibility (abbreviated ms) of G is the largest such d over all possible orderings of the edges. We will alter the premise a bit to talk about the cycle matching number of a graph ordering and define the cycle matching sequencibility (abbreviated cms) of a graph.<\/p>\n

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Feburary 22<\/strong>
\nAnna Mummert (Marshall)
\nStudying the recovery procedure for the time-dependent transmission rate in epidemic models<\/p>\n

Abstract:<\/em> In this talk I will discuss recent results on recovering the time-dependent transmission function for classical disease models given the disease incidence data. The recovery procedure is applied to a homogeneous population, meaning all individuals are equally likely to transmit the disease to any other individual. For a homogeneous epidemic model, there is one time-dependent transmission function. Also, the procedure is applied to a two population model, which has up to four distinct transmission functions. A two population model is appropriate for studying disease transmission in a heterogeneous population, for example, a population split into children and adults, who spread the disease differently among themselves. Determining the time-dependent transmission function that exactly reproduces disease incidence data can yield useful information about disease outbreaks, including a range potential values for the recovery rate of the disease and offers a method to test the \u201cschool year\u201d hypothesis (seasonality) for disease transmission.<\/p>\n

This will be a general audience talk. The talk will end with a discussion of several research projects that would be appropriate for a capstone project or a Master\u2019s thesis.<\/p>\n

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March 7<\/strong>
\nMatthew Sedlock (Johns Hopkins University)
\nPercolation models<\/p>\n

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March 9<\/strong>
\nAvishek Mallick (University of New Hampshire)
\nInferential procedures based on samples with non-detects from normal and related distributions<\/p>\n

Abstract:<\/em> In this presentation, I am going to talk about the problems of computing confidence interval, tolerance interval and prediction interval based on the samples with non-detectable values, i.e. Type I censored samples from Normal and related distributions. Firstly two types of imputation approach has been investigated: one based on the maximum likelihood estimates (MLEs) of the parameters, and the second uses some ad hoc estimates, that are particularly suitable for sample sizes that are small or moderately large. Monte Carlo simulation is used to investigate the performance of these procedures. For a given percentage of values below the DL, this proposed imputation approach exhibits excellent performance when the sample size is small to moderately large. However, as the sample size gets large, the ad hoc procedure performs poorly; but the MLE based procedure continues to perform reasonably well unless the sample size gets very large. However, the confi\u0081dence levels can be calibrated so that the MLE based imputation approach continues to provide coverage probabilities close to the nominal level.<\/p>\n

I will also talk about the inferential problems concerning the mean and the quantiles of a lognormal distribution based on a Type I censored sample. Here procedures based on generalized confi\u0081dence intervals and modifi\u0081ed signed log-likelihood ratio test (MSLRT) statistics are used. Performance of these two procedures along with that of the signed log-likelihood ratio test (SLRT) statistic is compared using Monte Carlo simulation. Based on numerical results, it is found that the generalized confidence interval and the MSLRT based confidence interval are both satisfactory for inference concerning a lognormal quantile, when the percentage of non-detects is fairly large, as large as 70%. However, the conclusion is not so clear cut for inference on the lognormal mean. In fact, this work shows that the routine application of the MSLRT must be approached with caution, the procedure may even give results that are less satisfactory compared to the SLRT based solution. A final point to note is that the generalized confidence interval idea is easier to understand and implement, especially for a practitioner, and it provides accuracy very similar to that of the MSLRT for estimating the lognormal quantiles. For each of the problems considered, the results the illustrated using practical examples.<\/p>\n

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March 12<\/strong>
\nMyung Soon Song (University of Pittsburgh)
\nAn unconventional approach to likelihood of correlation matrices<\/p>\n

Abstract:<\/em> Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analyses are studied. A multivariate numerical integration method for developing a better approximation of the likelihood of correlation matrices is studied. Analyses for (1) intercorrelations among Math, Spacial and Verbal scores in an SAT exam and (2) intercorrelations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Algorithms to evaluate likelihood and to find the MLE is developed. Comparison with two conventional methods (joint asymptotic weighted average and marginal asymptotic weighted average) is shown.<\/p>\n

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April 2<\/strong>
\nSharad Silwal (Kansas State University)
\nImage quality assessment methods<\/p>\n

Abstract:<\/em> The central problem in our presentation is the following: Suppose we have an image and we want to find the best match to this reference image from a large database of images. The best way to tackle this problem is indeed to let human observers, the ultimate receivers of all image information, be the judge. However, due to the tedious and time-consuming nature of this problem, we would rather employ a computer algorithm which mimics the human visual system in recognizing similarity between images. In this presentation, we will describe some of the challenges of this problem and discuss some image quality assessment methods which attempt to address these challenges. In particular, we will see how tools from Statistics and Fourier Analysis can come into play in the development of such methods.<\/p>\n

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April 6<\/strong>
\nJiYoon Jung (University of Kentucky)
\nThe topology of restricted partition posets PDF<\/p>\n

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2011 Fall Math Colloquia<\/h2>\n
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November 8<\/strong>
\nCarl Mummert (Marshall)
\nTwo examples from infinitary combinatorics<\/p>\n

Abstract:<\/em> I will talk about two results in infinitary combinatorics, Ramsey\u2019s theorem and Hindman\u2019s theorem. These results show that certain types of structure in the natural numbers cannot be destroyed by partitioning the set of natural numbers into a finite number of pieces. I will also discuss the recent interest in these combinatorial theorems by researchers in mathematical logic. The talk will be aimed at undergraduates, and no previous knowledge of combinatorics is necessary. All students are welcome.<\/p>\n

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2011 Spring Math Colloquia<\/h2>\n
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April 5<\/strong>
\nSuman Sanyal (Marshall)
\nStochastic Dynamic Equations<\/p>\n

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April 8<\/strong>
\nElizabeth Niese (Virginia Tech)
\nMacdonald polynomials and the hook-length formula for standard Young tableaux<\/p>\n

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April 15<\/strong>
\nAndrew Oster (\u00c9cole Normale Sup\u00e9rieure)
\nA laminar model for the development of the primary visual cortex<\/p>\n

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April 18<\/strong>
\nMichael Schroeder (University of Wisconsin-Madison)
\nPhi-symmetric Hailton cycle decompositions of graphs<\/p>\n

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April 20<\/strong>
\nRemy Friends Ndangali (University of Florida)
\nBound states in the radiation continuum and nonlinear effects in photonic structures<\/p>\n

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April 22<\/strong>
\nPaul Shafer (Cornell)
\nCoding arithmetic in the Medvedev degrees and its substructures<\/p>\n

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2010 Fall Math Colloquia<\/h2>\n
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September 8<\/strong>
\nAnna Mummert (Marshall)
\nGet the News Out Loudly and Quickly: Modeling the Influence of the Media on Limiting Infectious Disease Outbreaks<\/p>\n

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October 13<\/strong>
\nCarl Mummert (Marshall)
\nThe axiom of choice in mathematics and computability<\/p>\n

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November 9<\/strong>
\nSuman Sanyal (Marshall)
\nStochastic Process Indexed by Time Scale<\/p>\n

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2010 Spring Math Colloquia<\/h2>\n
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February 10<\/strong>
\nAnna Mummert (Marshall)
\nParameter sensitivity analysis for mathematical modeling<\/p>\n

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April 14<\/strong>
\nSuman Sanyal (Marshall)
\nStochastic dynamic equations and their applications<\/p>\n

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April 21<\/strong>
\nJohn Drost (Marshall)
\nInheritance, bankruptcy, and the Talmud<\/p>\n

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2009 Fall Math Colloquia<\/h2>\n
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September 16<\/strong>
\nCarl Mummert (Marshall)
\nGaming around with topology<\/p>\n

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October 15<\/strong>
\nSydney Thembinkosi Mkhatshwa (Marshall)
\nSuper-spreading events<\/p>\n

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November 11<\/strong>
\nDuane Farnsworth (Marshall)
\nApproximation Numbers and Ideals of Operators<\/p>\n

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2006 Fall Math Colloquia<\/h2>\n
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October 19<\/strong>
\nPeter Saveliev (Marshall)
\nLow level vision through topological glasses<\/p>\n

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2005 Spring Math Colloquia<\/h2>\n
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February 22<\/strong>
\nNorah Esty (University of California – Berkeley)
\nTopological Properties of Orbit Sets for Groups of Homeomorphisms<\/p>\n

Abstract:<\/em> In this talk, I will introduce some dynamical systems by looking at some examples of the way a homeomorphism can iterate a point on the circle, from fixing points and having periodic orbits to creating dense orbits. I will go over the complete classification of orbit types given by the Poincare Classification Theorem, including the existence of homeomorphisms with an invariant Cantor set. Then I will discuss the analogy between the iterate set for a single homeo (corresponding to an action of the group Z) and the orbit set of more general groups of homeomorphisms. Sacksteder\u2019s Theorem gives three possibilities for a particular group G. Sacksteder\u2019s first case is the existence of a finite orbit, however, it does not give nay information about the orbit type of the remaining points. My work expands this case to examine what happens to all others point on the circle when the group has a common periodic set.<\/p>\n

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February 24<\/strong>
\nElmas Irmak (Michigan State University)
\nMapping Class Groups<\/p>\n

Abstract:<\/em> I will talk about the mapping class groups of compact, connected, orientable surfaces. I will discuss how combinatorics of different curve complexes on surfaces is used to study the algebraic structure of the mapping class groups.<\/p>\n

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March 3<\/strong>
\nAkhtar Khan (Michigan Technological University)
\nAn inverse problem in elasticity<\/p>\n

Abstract:<\/em> In this talk I will discuss a simple inverse problem in elasticity. The talk will be focused on the issues such as: What is an inverse problem? What are the common approaches to solve an inverse problem? Why are inverse problems challenging? I will pose the inverse problem as an optimization problem and discuss several existing approaches. Numerical results will be given for the various approaches. Having established this background I will discuss some new results obtained by myself. Mainly I will show that the output least-squares approach for elliptic inverse problems, using a coefficient-dependent energy norm functional, results in a smooth, convex minimization problem. I will discuss several theoretical and numerical advantages of having a convex objective functional. The issue of dealing with the discontinuous coefficients will also be discussed.<\/p>\n

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April 8<\/strong>
\nJudith Silver
\nConics in Projective Geometry<\/p>\n

Abstract:<\/em> The definition of a conic usually requires the concept of distance; but in projective geometry, conics are determined in a metric-free way. This talk will show how such conics are formed, using Geometer\u2019s Sketchpad and some audience participation. All of the material should be accessible to students, as well as faculty.<\/p>\n

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April 22<\/strong>
\nBonnie Shook
\nTopological Approaches to Fingerprint Identification<\/p>\n

Abstract:<\/em> In this talk, I will analyze the topology of different types of fingerprints in order to find a new tool to assist in computer identification. I will focus on the homology groups of the main types of fingerprints \u2013 loops, whorls, and arches \u2013 and their variations. I will examine if there are fundamental differences between the homological features of these types.<\/p>\n

Nathan Cantrell
\nCubical Homology in Medical Imaging<\/p>\n

Abstract:<\/em> Trabecular bone architecture is extremely important in early recognition of estrogen loss and osteoporosis, as loss of bone connectivity is one of the earliest signs of disease. Moreover, intense research is underway to quantify and understand the relationship between trabecular architecture and its mechanical properties for the benefit of both medicine and bio-engineering. Such a complex structure which appears as an evolutionary adaptation to the external forces acting on the bone is extremely difficult to examine quantitatively. Topology, however, may be able to reveal significant characteristics of this network. Is there a correlation between orientation and connectivity of the network and bone strength? The voxelized data produced by \u03bc-MR or \u03bc-CT is ideal for cubical homology, a relatively young homological method. In short, the technique uses the boundaries of cubical building blocks to expose these topological features and simplify certain information into an extremely finite amount of data. Cubical homology and computational abilities are now beginning to coalesce providing enormous implications for the cubical format of computer graphics and medical imaging.<\/p>\n

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April 29<\/strong>
\nArthur Porter (Professor Emeritus, University of Toronto)
\nManchester University’s Contributions to Analog and Digital Computing<\/p>\n

Abstract:<\/em> Dr. Porter will discuss the role Manchester University played in the development of computing and computer applications. His talk will include the following topics:<\/p>\n