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