The Advanced Research Initiative of the Department of Mathematics and College of Science invites distinguished researchers to Marshall to speak with both general and specialized audiences and interact with graduate and undergraduate students. The speaker for Fall 2016 is Dr. Richard Ehrenborg from the University of Kentucky. As well as being a distinguished mathematician in the area of combinatorics, coalgebras, geometry, invariant theory, probability, and stochastic processes, Ehrenborg is also an avid juggler and magician.

He will give two presentations:

**Title: Mathematical Magic**

*Time and Date:* Monday, October 10, 2016 at 4 p.m. in Corbly Hall 104

*Abstract: *We will demonstrate a few “magic” tricks, all based upon mathematics. We will reveal the tricks including the mathematics behind them. Among other topics this will include parity, recursions and Hall’s Marriage Theorem.

**Title: Counting Permutations with Calculus**

*Time and Date:* Tuesday, October 11, 2016 at 4 p.m. in Smith Hall 516

*Abstract:* A permutation pi = pi_1 pi_2 … pi_n is a list of the elements 1 through n in some order. A permutation is alternating if the elements zig-zag, that is, pi_1 < \pi_2 > pi_3 < … .

We prove a classic formula for the number of alternating permutations using the interplay of geometry and calculus. Using the same techniques we also study the number permutations with no double ascents, that is, there is no index i such that pi_i < pi_{i+1} < pi_{i+2}.

Unfortunately, this last case becomes messy and leads to open questions as to where else these techniques can be applied.