Thursday, November 16, 20174:00PM - Thursday, November 16, 20175:00PM
At Ruffner 356
Speaker: Arnold Yim
Abstract: Given a cake, if you makes n cuts, how many pieces will you have? The answer depends rather much on exactly how we make the cuts. Using a counting technique called "deletion-restriction," one can give a recursive answer. This in turn can be used to determine how to make the maximum number of pieces with n cuts, and what that number is.
Seemingly unrelated, if we are given a graph, one might consider the ways to color the vertices of the graph while making sure that adjacent vertices have different colors. Interestingly, we can also count the number of ways using "deletion-restriction."
In yet a different setup, the ideas behind "deletion-restriction" show up when one looks at flows (that is, vector fields) which are tangent to a collection of planes in space. Intriguingly, the study of these flows can actually help us answer our counting problems.
The talk will explain the connections between cutting, coloring, and flowing, by way of pictures and examples.
Bio: Arnold Yim is currently a math professor at Bridgewater College. He earned his PhD in mathematics from Purdue University in 2016. His area of research is algebraic geometry; in particular he studies hyperplane arrangements, tropical geometry, and dynamical systems.
We meet for a social with the speaker from 3:30 to 4:00. Presentations are from 4:00-5:00 p.m. in Ruffner 356. Please join us!