Columbia Undergraduate Math Society

Fall 2023 <<  Spring 2024 Lectures >> Summer 2024

Wednesdays, 7:30 pm; Room 520 Math Building
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The Columbia Undergraduate Mathematics Society has the purpose of exposing members to different topics or areas of research in mathematics that they might not otherwise encounter in class. The lectures should be accessible to all students studying mathematics or pursuing math-related majors. Everyone is welcome!

Date Speaker Title Abstract
January 31
Social Event
 
 
February 7
Gyujin Oh
Arithmetic groups vs. mapping class groups
Integer-coefficient matrix groups, like SL_2(Z) (referred to as arithmetic groups), play crucial roles in number theory, representation theory, and arithmetic algebraic geometry. On the flip side, mapping class groups are key players in low-dimensional topology and Teichmuller theory. Despite their distinct origins, these groups share significant similarities. This talk will explore these analogies.
February 14
Peter Woit
Spinors and Twistors
Instead of using vectors to do geometry, in any dimension one can use spinors, which in some sense are "square roots" of vectors. In four dimensions these have unusual properties, crucial for understanding four-manifolds in Riemannian geometry, and special relativity in physics. Also in four dimensions, pairs of spinors occur as twistors, with the twistor geometry explaining how conformal symmetry works in four dimensions. I'll try and explain both the mathematics and some of the implications for physics.
February 21
Soren Galatius
Graph complexes and their applications
Graph complexes are fairly elementary to define.  Nevertheless, there are many elementary-sounding questions about them which we cannot answer yet.  Since they were introduced in the 1990s, they have made appearances in several seemingly rather different areas of mathematics.  I will explain the definition and some applications of these intriguing objects.
February 28
Alan Zhao
Hilbert's Tenth Problem
Yuri Matiyasevich's book "Hilbert's Tenth Problem" explains the negative resolution of Hilbert's question of whether or not a general algorithm to solve Diophantine equations. The book produces surprise after surprise in just its first three chapters, and in just its fourth chapter constructs an "NP-hard" Diophantine equation: the solvability of any Diophantine equation reduces to this one. This talk will highlight these results, and moreover the completely elementary nature of the proofs involved.
March 6
Alex Scheffelin
 
 
March 13
 
Spring Break
 
March 20
Milind Hegde
 
 
March 27
 
 
 
April 3
Jingbo Wan
 
 
April 10
Morena Porzio
 
 
April 17
Henry Segerman
 
 
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