GROW 2017 Talk Titles and Abstracts
Title: Can you hear the shape of a drum?
Abstract: When you hit a drum it vibrates at a certain set of overtones, or fundamental frequencies. In this talk I'll ask the question: if two drums have the same set of overtones do they have the same shape? I will first discuss how the overtones of a plucked string determine its length. I'll then move on to higher dimensions and state the problem as a partial differential equation. Finally, I'll discuss partial answers to the question, including very recent work, as well as what parts still remain unanswered.
Title: Pasting polynomials together
Abstract: Given two polynomials, we can try to mathematically "paste them together" to obtain a rational function through a procedure known as mating the polynomials. In this talk, we will begin with the complex numbers and try to understand the "shape" of complex polynomials in general. We will then discuss the mating of two quadratic polynomials: we explore examples where the mating does exist, and examples where it does not. There will be lots of exploration, discovery, and movies in this talk.
Banquet Keynote Address
Title: My Path Towards And In Mathematics.
Abstract: Although My B.Sc. and Ph.D. degrees are in physics rather than mathematics, I have lived most of my professional career as a mathematician. The talk will describe how this transition happened, as well as several other stages in my mathematical life.
Title: Discrete approximations
Abstract: In calculus, many functions of interest (such as the exponential, sine, and cosine functions) are not polynomials, but they are approximated arbitrarily well around any point by certain polynomials leading to the Taylor series. In this talk I'll discuss approximations not to functions but to curves, surfaces, and their higher-dimensional counterparts, manifolds. The role of polynomials is replaced by another discrete object, the simplicial complex. I'll explain what these are, how to use them. and why mathematicians care about them.