Topics in Mathematical Physics (520-1-41)

Instructors

Eric Zaslow
8474676447
Lunt 302

Meeting Info

Lunt Hall 102: Mon, Wed, Fri 11:00AM - 11:50AM

Overview of class

Title: q-difference equations in math and physics

This course will indulge my recent interest in q-difference equations. I hope the area is sufficiently rich to be worth our while! The idea is for you, the students, to explain small(ish) pieces of the story in your presentations, as outlined below. Together we will try to connect these parts.

The rough plan is this. Each student will give roughly 25 presentations, limited in length to 30 minutes. (The decreasing function 25/n may be an inducement to recruit friends, just sayin'.) Each student will be required to ask or answer at least one question each class. These questions and discussion will comprise the other 20 minutes, some before and some after the presentation.

Here is a non-exhaustive list of possible topics, with some references. Each could accommodate multiple (many!) presentations.

* Differential equations with regular and irregular singularities; monodromy and Stokes phenomena. Reference: "The Painlevé Property,"

https://link.springer.com/chapter/10.1007/978-1-4612-1532-5_2

* Isomonodromic deformations; Schlesinger equations

* The Painlevé property; Painlevé equations.

* q-Painlevé equations, after Jimbo and Sakai

* Quantum cohomology, Frobenius manifolds (Dubrovin)

* Quantum cohomology of P^2 and P_{VI}, after Dubrovin, Hitchin, Kontsevich-Manin

* Quantum mirror curves and q-difference equations

* Topological String / Spectral Theory duality, after Grassi-Hatsuda-Mari\~no, Aganagic-Cheng-Dijkgaaf-Krefl-Vafa.

* DT Theory and Riemann-Hilbert problems, after Bridgeland

Class Materials (Required)

No required or suggested textbooks

Class Materials (Suggested)

No required or suggested textbooks