We are a graduate-student run seminar showcasing special topics in geometry and topology at large. Talks in this seminar often involve
Differentiable/Riemannian geometry, analysis on manifolds, and metric spaces. There have also been talks in topological data analysis and sheaf theory.
Graduate students at all levels are welcome to participate. The graduate student seminars are opportunities to practice talks before a conference, or to
present something interesting to share among friends. After all, the best way to learn something is to teach it!
Fall 2024
We meet on Mondays, 1:00 to 1:50 PM, in Lincoln Hall 1027.
Recent Talks
Boundaries of Hyperbolic Spaces and CAT(0) Spaces
Manisha Garg
I will give an introduction to the boundaries of CAT(0) spaces and hyperbolic Spaces. I will present the topology endowed on the boundary and the interesting metric spaces like Cantor sets that occur as boundaries. I will also state results related to various metric and topological dimensions of boundaries.
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An Introduction to Khovanov Homology
Jonathan Higgins
The Jones polynomial is a well-known link invariant, discovered by Vaughan Jones in the 80s. It is very handy in low-dimensional topology, as it admits an easy combinatorial method for computation. We begin by describing how to compute it via the Kaufmann state model and cube of resolutions. We then proceed to construct a homology theory, known as Khovanov homology, whose graded Euler characteristic is the Jones polynomial and which gives a stronger invariant. This provides a glimpse into the vast world of topological quantum field theories (TQFTs) and categorification.
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Distribution Theoretic Semantics for Non-Smooth Differentiable Programming
Chris Lam
With the rise in differentiable learning methods and differentiable ray tracing algorithms, computer scientists have begun turning their attention towards algorithms and semantics for differentiation operators. The major victory on this front has been the development of the theory of automatic differentiation, which efficiently computes derivatives of functions in very high dimensions via repeated applications of the chain rule along with some computation saving tricks. However, because this algorithm is inductively defined on the syntax of the language, it is vulnerable to two failure cases...
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