Wednesdays, 7:30 pm; Room 520 Math Building
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Click here for information on the Spring 2024 Proof Workshop
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 mathrelated majors. Everyone is welcome!
Date  Speaker  Title  Abstract 
January 31 
Social Event



February 7 
Gyujin Oh

Arithmetic groups vs. mapping class groups 
Integercoefficient 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 lowdimensional 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 fourmanifolds 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 elementarysounding 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 "NPhard" 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

