Past Semesters

Spring 2023

I) I’m participating in a seminar led by Andrey Smirnov on equivariant cohomology/quiver varieties. I will present at least once.

II) I’m mainly reading two textbooks, Kirilov’s “Quiver representations and quiver varieties” and Tu’s “Introduction to equivariant cohomology”.

III) I’m participating in a seminar led by Jiuzu Hong and Prakash Belkale on the Riemann-Hilbert correspondence. I’m following along but not supremely closely. I may or may not give a presentation.

Fall 2022: 

I) Most of my free time will be spent reading this book “Superschool on Derived Categories and D-branes”, edited by Ballard, Doran, Favero and Sharpe. The notes are presented in 3 parts, a primer on categorical methods in algebraic geometry involving derived and triangulated categories, first approaches toward mirror symmetry, and physical considerations, namely string theory and D-branes. Reading this book is part of my ongoing attempt to break into mathematical physics/string theory.

II) I’m taking a course at Duke taught by Paul Aspinwall focused on the mathematics of quantum mechanics and string theory. The homepage for the course can be found here. I’m also typing lecture notes for the course, which can be found here.

III) I’m participating in a reading group on chapters II and III of Hartshorne, led by Prakash Belkale of UNC.

Summer 2022:

I) The main thing I’m doing over the summer is studying to pass the comprehensive(/qual/prelim) exams in August. This involves studying the standard first year sequences and practicing many problems in the areas of manifolds, algebraic topology, real and complex analysis and abstract algebra.

II) Following along several mini courses as part of UT’s summer mini course program. These include courses on Fukaya categories, Lie groupoids and differentiable stacks, and topological field theory.

Spring 2022:

I) Seminar focused on understanding how to use stacks in algebraic geometry. We are reading notes from Vistoli on his homepage titled: “Notes on Grothendieck topologies, fibered categories and descent theory.” It looks like we will finish the entire pdf by the end of semester. Organized by Dr. Jiuzu Hong.

II) Seminar very loosely focused around “homological algebra part II” (continued from previous semester), though we kind of discuss whatever we want. Topics so far have included derived categories, Hoschild (co)homology and Lie algebra cohomology. Halfway through this semester, we shifted the focus to mathematical physics. Currently we are discussing field theory with the short term goal of learning about supersymmetric quantum mechanics and morse theory, and a long term goal of discussing topological strings and branes. Organized by Dr. Lev Rozansky.

III) Online seminar/mini-course taught by Dr. Gurbir Dhillon as part of the Yale algebra and geometry series centered on an introduction categorical representation theory and the Langlands program. Here is the organizing website link. Notes featured in Notes section.