Arya Vadnere

Ph.D. candidate, Department of Mathematics, University at Buffalo

Title: Mathematical Billiards

Abstract: Suppose you have a point-sized ball gliding on a billiard table with a frictionless surface. The trajectory ends if it goes into a hole, and if it hits the boundary of the table, the ball follows the standard laws of reflection (the angle of incidence is the same as the angle of reflection). Depending on the shape of the table, we can ask several questions - how many times can the ball hit a wall before it goes into a hole? In particular, what is the sequence of sides the ball hits? Can it come back to where it started, and keep looping its path in a periodic motion? Is the trajectory of the ball dense inside your shape? 

Studying such questions gives deep insights on geometric structures on surfaces and their dynamical properties. In this talk, we shall try to answer some of these questions and discuss some related open questions. This talk shall require no prerequisites, and should be fairly interactive, so come with your thinking caps on!

Alexander Bivolcic

Ph.D. candidate, Department of Mathematics, University at Buffalo

Title: Water Waves and Differential Equations

Abstract: Most mathematics students are exposed to basic applications in elementary calculus classes. However, the relation between differential equations and physical phenomena is not covered until senior level classes. This talk will begin by discussing simple differential equations which students may have seen before. We will then discuss linear wave equations which come up in most physics or mathematics classes. Finally, we will discuss nonlinear water wave equations. We will discuss what makes them so challenging to solve as well as the types of phenomena they have been found to produce.

Dr. Christine Uhl

Associate Professor, Department of Mathematics, St. Bonaventure University

Title: Grids, Graphs, Greatness

Abstract: Don’t you love when you can play a game, and it turns out to hold some great mathematics?  We will start with a simple game that can be played on a grid and then translate it into a graph theory problem.  We will define the problem of finding the metric dimension of a graph, and will show a constructive approach to solving a family of a direct product of three complete graphs.

Dr. Tyrone Ghaswala

Lecturer, Center for Education in Mathematics and Computing, University of Waterloo

Title: Getting tangled up with the rationals

Abstract: Ever heard an elder relative insist that π is 22/7? We will explore some cool facts about continued fractions, and see why that relative isn't that far off! The talk will also take a tour through an unlikely connection between rational numbers and tangles.