The Warmup Program for entering first-year graduate students in mathematics is a sequence of social and academic events organized by senior graduate students in the Math department. The goals of the 2025 program are to inform incoming graduate students about coursework, give an overview of research directions and content available in the department, provide opportunities for first-year students to meet senior graduate students, and develop a group dynamic among the first year cohort.
Please don't skip everything ! :-(
The discovery of hyperbolic geometry in the 19th century fundamentally reshaped our understanding of space. It can be viewed as the geometry in which Euclid’s parallel postulate fails—or equivalently, as the study of spaces of constant negative curvature. Hyperbolic space has many interesting features; in particular, it has a very rich group of isometries, allowing a huge variety of crystallographic symmetry patterns. This makes the geometry both rigid and flexible at the same time. Its properties and symmetries are closely related to tree-like growth patterns and fractals, suggestive of many natural biological objects like ferns and trees. In this talk, we will take a tour through some intriguing phenomena of hyperbolic geometry, with glimpses into the world of hyperbolic surfaces and 3-manifolds.
Location: Meet on Quad in front of Eckhart
Join the UChicago Association for Women in Math (AWM) for some crafts and taco bell. Students of all genders are welcome!Location: Meet on the front steps of Eckhart
We will start by introducing translation surfaces — flat surfaces with cone singularities and straight-line flow. These are among the simplest examples of dynamical systems, yet they model a variety of physical processes, such as Ehrenfest wind-tree models, polygonal billiards, optical cavities, and Eaton lenses. Most translation surfaces are chaotic, or, more specifically, uniquely ergodic in almost every direction: for almost every initial point, the straight trajectory equidistributes for area, and time averages equal space averages (this idea comes from Boltzmann's ergodic hypothesis in thermodynamics). After a primer where I will define everything we need, I will present a new construction on translation surfaces called branched slit \(n\)-cover: on a uniquely ergodic \(X\), pick a slit \( s=[P,\,Q] \); take \(n\) copies and switch sheets \( i\mapsto i+1 \pmod n \) each time the vertical flow hits \(s\) (i.e., glue the copies together). It turns out that the unique ergodicity property is robust and quantifiable under such covers despite localised branching. This is especially notable because conditions are mostly geometric despite the measure-theoretic core of the problem. (Joint with Elizaveta Shuvaeva.)
Location: Meet on the front steps of Eckhart