gigem cONFERENCE

Inaugurated in 2018, the Gathering In Graduate Expository Mathematics (GIGEM) is an annual conference organized during the spring semester by the AMS Graduate Student Chapter at Texas A&M University and hosted by the Department of Mathematics at Texas A&M University.

The talks are mostly expository in nature, so the speakers and the audience members are not expected to have any research experience. The conference is usually held on a Saturday and it comprises of two sessions: morning and afternoon. Each talk is 20 minutes long, followed by a 5-minute Q/A session. 

9:00 am - Breakfast

9:30 am - Garrett Tresch

Title: Properties of Graphs and Metric Embeddings

Abstract: Many graph algorithms utilize low distortion embeddings into Banach spaces where the addition of linear structure can aid in approximation. While in many cases the worst possible distortion is known, with additional knowledge on the geometry of our underlying graph these embeddings can often be vastly improved. So join me as we explore a Willy Wonka factory of metric geometry... where popular graph properties enter (bright eyed students) and optimal embeddings into some of your (my) favorite spaces come out (kids with everlasting trauma). *BYOC (Bring Your Own Candy)

10:00 am - Chris Pecoraro

Title: Compressible Euler and its Low Mach Limit

Abstract: In this talk I will give a brief overview of the compressible Euler equations and some of its properties. In particular, the Euler equations can be written in terms of a non dimensional constant, called the Mach number, that characterizes the flows present. The limiting behavior of the system as the Mach number approaches zero is quite complex. A formal exposition of this limiting process will be given.

10:30 am - Jordy Lopez Garcia

Title: Algebraic Fermi curves

Abstract: Bloch and Fermi varieties arise in the spectral theory of operators on periodic media. Although these varieties are analytic in nature, by discretizing to operators on periodic graphs, they can be regarded as algebraic varieties. Thus, a number of physically important properties can be studied using strong methods from algebraic geometry. In this talk, I will describe some of the tools we use to study these varieties.

11:00 am - Aatmun Baxi

Title: Fusion Categories as a Generalization of Finite Groups

Abstract: Fusion categories (FCs) appeared in the study of conformal field theories. Later, it was found that they enjoy connections to quantum topology and condensed matter physics, among others. One such mathematical connection is their interpretation as generalizations of finite groups and their behavior over ℂ. We present this view, placing a strong emphasis on the intuitive algebraic behavior of FCs. No familiarity is assumed apart from basic definitions in category theory.

11:30 am - Inyoung Ryu

Title: Nielsen–Thurston classification

Abstract: As a mapping class group of a hyperbolic surface acts on Teichmüller space, it changes the geometric structure of the surface. Moreover, all mapping classes are classified into three types depending on how it changes the geometry. In this talk, I will explain these three types of mapping classes, and introduce Nielsen-Thurston classification theorem. 

12:00 pm - Erik Davis

Title: Goss L-Functions and Gamma Values

Abstract: A common theme in number theory is to take an arithmetic object and associate to it an L-function. In this talk, I will discuss the L-functions of Goss associated to the Hilbert-Blumenthal-Drinfeld (HBD) modules given by Sinha. Sinha's modules have period lattices generated by gamma values and so these gamma values will naturally arise as L-function values in this setting. Examples will be presented along with some conjectures. 

12:30 pm - Lunch

1:30 pm - Junchen Zhao

Title: An interpretation of the entropy formula and a non-commutative extension

Abstract: Have you ever wondered why the information entropy formula looks like that, and what is it really measuring? In this talk, I will present some explicit computations to show that entropy measures a rate at which the empirical distribution of independent random samples drawing from a given distribution µ concentrates around \mu; and that entropy also counts "macrostates". If time permits and there is sufficient interest among the audience, I will demonstrate how entropy in non-commutative probability theory extends these ideas. 

2:00 pm - Nicklas Day

Title: Symmetries, the Rolling Distribution, and G_2

Abstract: Lie groups arise as the symmetry groups of differential equations and distributions and play an integral role in the classification of these geometric objects. Lie algebras enjoy a functorial correspondence with Lie groups, and the classification of complex simple Lie algebras was completed by Killing and made rigorous by Cartan in 1894. The classification includes 4 infinite families and 5 mysterious "exceptional" Lie algebras. In this talk, we'll discuss the "rolling spheres" distribution, which should be intuitively accessible to all, investigating its symmetry group and connections to one of the exceptional Lie groups.

2:30 pm - Yongming Li

Title: Exponential sums and Nonlinear Schrödinger Equations

Abstract: The title and the talk will be motivated by Jean Bourgain's paper (same title) where he used analytic number theory techniques in dispersive PDEs.

3:00 pm - Seth Hoisington

Title: The Math of Relativity

Abstract: We will discuss the standard mathematical formulation of special and general relativity with the goal of providing an intuitive understanding of Lorentzian spacetime and Einstein's Equation through a discussion of curvature, connections, Lorentz transformations, and (pseudo-)Riemannian manifolds

3:30 pm - Conference Concludes