Informal Mathematical Physics Seminar

organized by Igor Krichever and Andrei Okounkov

Mondays, 5:30, Room 507

To sign up for dinner click here

Schedule of talks for Spring 2017:

Feb 6 Changjian Su Chern-Schwartz-MacPherson classes, characteristic cycles and stable envelopes
Feb 13 no seminar (?)
Feb 20 Semen Artamonov A q,t-Integrable System on a Genus Two Surface
Feb 27 no seminar (?)
March 6
Shotaro Makisumi
March 13 spring break

March 20 Barton Zwiebach
March 27 no seminar (?)
April 4 Alexander Zamolodchikov

A note to the speakers: this is an informal seminar, meaning that the talks are longer than usual (1:30) and are expected to include a good introduction to the subject as well as a maximally accessible (i.e. minimally general & minimally technical) discussion of the main result. The bulk of the audience is typically formed by beginning graduate students. Blackboard talks are are particularly encouraged.

Abstracts

February 6
The Chern-Schwartz-MacPherson (CSM) class theory is a Chern class theory for singular varieties, whose existence is established by MacPherson. Motivated by another construction of Ginzburg and the relation between the CSM classes of Schubert varieties and stable envelopes, we give another formula for the CSM classes for a general variety using the characteristic cycle associated to constructible functions. This is joint work with P. Aluffi, L. Mihalcea and J. Schuermann.

February 20
In my talk I will consider a quantum integrable system with two generic complex parameters q,t whose classical phase space is the moduli space of flat SU(2) connections on a genus two surface. This system and its eigenfunctions provide genus two generalizations of the trigonometric Ruijsenaars-Schneider model and Macdonald polynomials, respectively. I will show that the Mapping Class Group of a genus two surface acts by outer automorphisms of the algebra of operators of this system. Therefore this algebra can be viewed as a genus two generalization of A_1 spherical DAHA. (This is joint work with Shamil Shakirov)

Seminar arxiv: Fall 2016 Spring 2016 Fall 2015 Spring 2015 Fall 2014 Spring 2014 Fall 2013 Spring 2013 Fall 2012 Spring 2012