## GROW 2017 Talk Titles and Abstracts

#### Friday, October 13, 4:00pm-5:00pm

Student Seminar

Perry Kleinhenz

**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.

#### Saturday, October 14, 9:45am-10:30am

Research Lecture

**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.

Pasting polynomials together talk slides

#### Saturday, October 14, 2:00pm-2:45pm

Research Lecture

**Title:**Lively Networks

**Abstract:**Many systems -- including living cells -- exhibit collective behaviors that emerge from complex networks of many interacting processes. What can the ``wiring diagram'' of those interactions tell us about the dynamics of the system, and can we deduce the underlying network from the collective dynamics? In this talk, I will discuss what we can learn about the dynamics of interacting systems from the topology of the underlying network of interactions.

#### Saturday, October 14, 6:00pm

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.

#### Sunday, October 15, 9:15am-10:00am

Research Lecture

**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.