Related papers: The theta correspondence over finite fields
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
A sub-relation of the $\Theta$-correspondence called the \emph{$\eta$-correspondence} is defined by Gurevich-Howe for a finite reductive dual pair in stable range. In this paper we propose an extension of the correspondence to general…
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…
This work is a survey of relations between Drinfeld modules and higher dimensional fields of positive characteristic. The main new result stated is the expression of vanishing orders of certain modular forms through partial zeta values.
We give a complete theta expression of a pair of Hermitian modular forms as an inverse period mapping of lattice polarized $K3$ surfaces. Our result gives a non-trivial relation among moduli of $K3$ surfaces, theta functions and the finite…
In this paper we compute the multiplicities appearing in the ${\overline{\mathbb{F}}_\ell}$-modular theta correspondence in type II over a non-archimedean field $\mathrm{F}$, where $\ell$ is a prime not dividing the residue cardinality of…
Notes from a course given at Oujda university, Morocco, october 2002 - march 2003 within the support of a fellowship from the Agence Universitaire de la Francophonie. These notes present a brief introduction to Connes' non commutative…
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
These are notes for my Takagi lecture at the University of Tokyo in November, 2016. I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p>0 and Lusztig's character formula. I explain…
These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…
There is a huge amount of work on different kinds of theta functions, the theta correspondence, cohomology classes coming from special Schwartz classes via theta distribution, and much more. The aim of this text is to try to find joint…
This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…
These notes are based on a series of lectures given by the author at the Centre Bernoulli (EPFL) in July 2016. They aim at illustrating the importance of the mod-$\ell$ cohomology of Deligne--Lusztig varieties in the modular representation…
The Langlands correspondence of GL(2,F) over a non-Archimedean local field F of characteristic 0 has been well studied. The construction uses the theta correspondence. In this paper, we are going to describe explicitly how this construction…
These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild…
These notes form an extended version of a minicourse delivered in Universite de Montreal (June 2002) within the framework of a NATO workshop ``Normal Forms, Bifurcations and Finiteness Problems in Differential Equations''. The focus is on…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
These are notes from a 3-lecture course given by V. Dokchitser at the ICTP in Trieste, Italy, 1st--5th of September 2014, as part of a graduate summer school on "L-functions and modular forms". The course is meant to serve as an…