Columbia Undergraduate Math Society

Summer 2018 << Fall 2018 Lectures >> Spring 2019

Wednesdays, 7:30pm; Room 507, Mathematics
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Date Speaker Title Abstract
September 12
Shizhang Li
Hypergeometric Series and
Igusa's Formula
Consider a 2nd order ODE: $z(1-z)f'' + (1-2z)f' - (1/4) f = 0$ known as hypergeometric differential equation. In the first part of my talk, I will briefly discuss it's solution found by Euler and studied systematically by Gauss known as Gauss hypergeometric series. Then, in the second part of my talk, I will discuss some seemingly completely unrelated formula (Igusa's formula) about counting points of Elliptic curves over characteristic $p$ (of Legendre form). For the rest of the talk, I will try to tell the audience why and how these two things are related.
September 19
Semen Rezchikov
Feynman Diagram Techniques
There is no reason why Feynman diagrams couldn't be taught in an advanced calculus class.  I will discuss something actually useful: how to compute asymptotic series for certain exponential integrals.  We will start with one variable, where the asymptotic series will be sums over graphs, and try to get to matrix integrals (the Feynman diagrams for which involve surfaces boundary, i.e. `interacting strings').
September 26
Ben Church
October 3
Alex Pieloch
October 10
Henry Liu
October 17
October 24
October 31
Stanislav Atanasov
November 7
Maithreya Sitaraman
November 14
November 21
No meeting
Thanksgiving Break
November 28
December 5
December 13
No meeting
Reading Week
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