Related papers: Lectures on Springer theories and orbital integral…

We present an explicit construction of cyclic cocycles on Cartan motion groups, which can be viewed as generalizations of orbital integrals. We show that the higher orbital integral on a real reductive group associated with a semisimple…

This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic…

PhD dissertation consists in three lines of investigation involving rational elliptic surfaces, namely 1) a study of conic bundles on these surfaces; 2) an investigation of the possible intersection numbers of two sections and 3) a theorem…

Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of…

We prove an integral version of the derived Springer correspondence for reduced motives. To achieve this result, we extend some results on reduced motives from schemes to quotient stacks with a finite number of orbits. More generally, we…

We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First,…

This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some…

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.

We generalize I. Frenkel's orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.

This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…

This article has two parallel perspectives: to demonstrate an inductive structure of Shalika germs, and to show an analogous inductive structure for affine Springer fibers. More precisely, we give an algorithm to compute arbitrary Shalika…

An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…

These are lecture notes for a mini-course given at the St. Petersburg School in Probability and Statistical Physics in June 2012. Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov…

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…

We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations,…

Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.

This is a summary of my lecture at Igor Frenkel's 70th birthday conference. I give a brief review of my almost forty years of scientific interactions with Igor. I focus here on three topics of joint interests: 2-cocycles, coadjoint orbits…

We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…