Spring 2025
January 30 -- Akiva Weinberger
Title: Hilbert's Tenth Problem Is Impossible
Abstract: Hilbert's tenth problem asks for whether there exists an algorithm to determine when Diophantine equations have solutions. In 1970, Matiyasevič showed that every computably enumerable set of numbers is Diophantine, answering Hilbert's question in the negative. I will give an overview of the techniques in the proof, which are mainly based on elementary number theory.
February 13 -- Tudor Popescu
Title: Using math to find love: perfect (or at the very least, stable) matchings, the marriage lemma, happy ending theorem, and some ongoing research
Abstract: In GSS's Valentine's Day Special Edition , we will present some famous combinatorics results, as well as some ongoing graph theory research.
February 27 -- Kamryn Spinelli
Title: Approximation of L-functions associated to Hecke cusp eigenforms
Abstract: In 2017, Matiyasevich described a strikingly effective method of approximating the Riemann zeta function using only a finite subset of its Euler factors. In the years since, several qualitative and quantitative properties of the approximation have been proven, and the technique has been adapted to Dirichlet L-functions, generating functions of divisor sums, and L-functions of elliptic curves. In this talk, we will summarize the history and ideas of the technique, outline new work extending it to the setting of L-functions of Hecke cusp eigenforms, and explain some observations which clarify some aspects of the construction. This is joint work with An Huang.
March 13 -- Kaitlin Ragosta
Title: A marking graph for finite-type Artin groups
Abstract: Finite-type Artin groups are a class of groups which include braid groups. Historically, many tools for studying these groups originated in the braid group setting and were later generalized to the remainder of the class. Since braid groups are mapping class groups, one could also ask which mapping class groups tools can be successfully extended to other finite-type Artin groups. In this talk, I will define a marking graph for finite-type Artin groups and discuss its similarities with the classical version.
April 10 -- Sarah Dennis
Title: Comparing the Perturbed Reynolds and Stokes Models for Thin Fluid Films
Abstract: I will talk about two corrected models for low Reynolds number flows.
I will outline the physics background for fluid dynamics. Then we can discuss the validity of assumptions underlying the adjusted/corrected models.
We will talk about some numerical methods for PDEs and I will show you some fun plots.
April 24 -- Anahita Babaie
Title: An Introduction to Optimal Transport
Abstract: In this talk, I will gently introduce the basic notions and some key results in optimal transport theory, including both the Monge and Kantorovich formulations. I’ll highlight fundamental concepts such as Wasserstein distance and duality, and conclude with a brief glimpse into the Wasserstein Gradient Flow.