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The Geometry & Topology Student Seminar aims to provide a relaxed environment where students can practice giving talks and learn about geometry and topology from other grad students and postdocs. We meet on Thursdays's 2-3PM in LCB 222. Below is our schedule for Fall semester.
The Geometry & Topology Student Seminar aims to provide a relaxed environment where students can practice giving talks and learn about geometry and topology from other grad students and postdocs. We meet on Thursdays's 2-3PM in LCB 222. Below is our schedule for Fall semester.
Organizers: Thomas Hill, George Shaji.
Organizers: Thomas Hill, George Shaji.
Fall 2025
Fall 2025
Sept 18: George Shaji
Title: A broad overview of infinite-type mapping class groups
Abstract: We will first look at the origin of the recent surge in interest in infinite type surfaces and then go over some of the basics of big mapping class groups using Rosendal's framework for Polish groups. As we explore the topic, we will also establish links to various other fields of research such as geometric and combinatorial group theory, dynamics and Teichmuller theory.
Sept 25: Harry Chen
Title: From fibrations of three manifolds to end periodic homeomorphisms of infinite type surfaces
Abstract: We begin with Thurston’s approach to representing cycles in H_2(M) with embedded surfaces and explore fibrations M^3 -> S^1 through the Thurston norm. We introduce the oriented sum of surfaces, and then illustrate how the sum of classes of fibrations within a fibered face again corresponds to a fibration. Finally, we show that limits of such sums give rise to homeomorphisms on infinite-type surfaces.
Oct 2: Minhua Cheng
Title: Dynamical cocycles and Lyapunov exponents
Abstract: Dynamical cocycles are a key tool for studying the linear behavior of a nonlinear system along its orbits. The Multiplicative Ergodic Theorem shows that this evolution has a very regular long-term structure: the space splits into directions where vectors grow or shrink at fixed exponential rates, called Lyapunov exponents. This structure helps us understand the stability of orbits and the geometry of the system. We will first introduce the key concepts with a motivating example and then explain the Multiplicative Ergodic Theorem. If time permits, we will explore some applications of this framework.
Oct 9: No seminar (Fall Break)
Oct 16: Yibo Zhai
Title: (TBA)
Abstract: (TBA)
Oct 23: Sage Yeager
Title: (TBA)
Abstract: (TBA)
Oct 30: Devanshi Merchant
Title: (TBA)
Abstract: (TBA)
Nov 6: Nilendu Das
Title: (TBA)
Abstract: (TBA)
Nov 13: Jorge Eduardo Gaspar Lara
Title: (TBA)
Abstract: (TBA)
Nov 20: Neelam
Title: (TBA)
Abstract: (TBA)
Nov 27: No seminar (Thanksgiving)
Dec 4: Jing Tao (AWM Speaker Series)
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