## Schedule

 Mon Tue Wed Thu Fri 10:30 - 11:30 x Losev Nadler Braden 13:30 - 14:30 Braden Losev POSTER Nadler 15:00 - 16:00 Losev Braden Williamson 16:30 - 17:30 Okounkov Okounkov Okounkov

If you click the name, you could watch the video of the lecture. (Okounkov's lectures are currently open only in Kyoto University.)
• ## Roman Bezrukavnikov (MIT, HSE International Laboratory of Representation Theory and Mathematical Physics)

### Categorification and dualities in representation theory

Abstract: I will start with discussion of Lusztig's theory of character sheaves and D-modules which will be presented as an example of categorification.

I will then talk about an approach to the affine analogue of this theory. Time permitting I will touch upon a (partly conjectural) relation to abelian subcategories in the derived categories of coherent sheaves.

• ## Tom Braden (University of Massachusetts, Amherst)

### Recent developments in modular sheaf theory

Abstract: Constructible sheaves on flag varieties, nilpotent cones, and related spaces have long played a central role in geometric approaches to representation theory. However, until recently they have almost always been taken with coefficients in a field of characteristic zero, in part because powerful tools from Hodge theory and D-modules are not available for sheaves with other coefficients. This mini-course will survey some of the recent applications of constructible sheaves with positive characteristic coefficients to modular representation theory, with emphasis on explicit examples and methods for computation.
• ## Ivan Losev (Northeastern University)

### Quantized quiver varieties

Abstract: Nakajima quiver varieties are remarkable symplectic algebraic varieties of interest for Geometric Representation theory, Algebraic Geometry and Mathematical Physics. Their quantizations are interesting associative algebras. I will discuss the representation theory of these quantizations and emphasize connections to the geometry.
• ## David Nadler (UC Berkeley)

### Elliptic character sheaves

Abstract: We will discuss approaches to character sheaves for loop groups via Geometric Langlands of the two-torus. For the spectral approach (appearing in preprints 1312.7164, 1312.7164), we will explain basic aspects of the microlocal geometry of coherent sheaves. For the automorphic approach (initial steps appearing in 1302.7053), we will focus on approaches to an elliptic horocycle transform. The results intertwine various strands joint with D. Ben-Zvi (Texas), P. Li (Berkeley), A. Preygel (Berkeley).
• ## Geordie Williamson (Max-Planck-Institut für Mathematik)

### Hodge theory and Soergel bimodules

Abstract: De Cataldo and Migliorini have given us a beautiful proof of the decomposition theorem using only classical Hodge theory. I will explain their proof and how one can adapt it to certain settings (Soergel bimodules) where the underlying space (and hence classical Hodge theory) might be missing. The positivity of the Hodge-Riemann relations is provided by simple positivity properties in Coxeter systems. Most of what I will discuss is joint work with Ben Elias.