Meeting Time: Friday, 3:005:00 p.m.  Location: 2135
Contact: Pavel Etingof and Victor Kac
Zoom Link: https://mit.zoom.us/j/93574730255
Meeting ID
944 6977 1032
For the Passcode, please contact Pavel Etingof at etingof@math.mit.edu.
Date and Time  Speaker  

September 6  Albert Schwarz (University of California, Davis) 
Geometric approach to quantum mechanics and quantum field theory In the geometric approach to quantum theory that I suggested several years ago we take as a starting point the set of states. This viewpoint is more general than the standard approach where the states are considered as density matrices and the algebraic approach where the states are identified with positive functionals on an associative algebra with involution. A large class of examples including conventional quantum mechanics can be constructed from classical theory where our devices can measure only a part of observables. Zoom Recording (Kerberos Required) 
Sept 13  Andrey Smirnov (The University of North Carolina at Chapel Hill) 
Frobenius intertwiners for qdifference equations The quantum difference equations are Ktheoretic analogs of Dubrovin connection in quantum cohomology.
In my talk I show that over $p$adic fields the quantum difference equations of Nakajima quiver varieties are equipped with the Frobenius automorphism $z\to z^p$. Zoom Recording (Kerberos Required) 
Sept 20  Student holiday  
Sept 27  Alexander Goncharov (Yale University) 
Exponential volumes in Geometry and Representation Theory Let S be a topological surface with holes. Let M(S,L) be the moduli space parametrising hyperbolic structures on S with geodesic boundary, and a given set L of lengths of the boundary circles. It carries the WeilPeterson volume form. The volumes of spaces M(S,L) are finite. M.Mirzakhani proved remarkable recursion formulas for them, related to several areas of Mathematics. Zoom Recording (Kerberos Required) 
Oct 4  Vasily Krylov (Harvard) Hunter Dinkins (MIT) 
Resolved Coulomb branches and vertex functions The first part of the talk will be given by Vasily Krylov and is based on the joint work with Ivan Perunov. We will discuss the geometry of Coulomb branches corresponding to finite Dynkin quivers. These Poisson varieties are known to be isomorphic to the socalled generalized slices in affine Grassmannians. Using the multiplication morphisms introduced by Braverman, Finkelberg, and Nakajima, we will construct coverings of resolutions of certain slices by affine spaces and, in particular, obtain explicit Darboux coordinates on them as well as characters of tangent spaces at torus fixed points. Zoom Recording (Kerberos Required) 
Oct 11  Ivan Losev (Yale) 
Categorical Heisenberg actions and modular representations of rational Cherednik algebras This is based on arXiv:2408.02485, joint with Bezrukavnikov. We construct certain functors on categories of representations of rational Cherednik algebras associated with symmetric groups in zero and large positive characteristic. Our functors are indexed by pairs of a partition and a rational number, the slope. For a given slope, the functors give an action of the positive half of the Heisenberg Lie algebra, while when the slope varies and the characteristic is positive we get a categorical action of the positive half of the elliptic Hall algebra. In this talk I will explain necessary notions, sketch the construction, and provide the motivation, partly coming from the double affine representation theory. 
Oct 18  Retreat  
Oct 25  Andrei Ionov (Boston College) 

Nov 1  Vera Serganova (University of California, Berkeley) 

Nov 8  Eric Opdam (University of Amsterdam) 

Nov 15  Yakov Varshavsky (Hebrew University of Jerusalem) 

Nov 22  Nathan Haouzi (Institute for Advanced Study) 

Nov 29  Thanksgiving  
Dec 6 