相关论文: Hilbert modular forms and their applications

We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes…

This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).

This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.

These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…

Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.

This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.

This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.

This is a review article on modular categories, extending an invited talk given at the workshop "Categorical (co)algebraic methods in quantum informatics and linguistics", Oxford, October 29-31, 2010. To appear in C. Heunen, M. Sadrzadeh,…

This is the text of a talk to the study week on \emph{Modular forms and Galois representations} held in Luminy, 1997. We give a survey of $p$-adic modular forms, as developped by Serre, Katz, Hida, Wiles, Coleman and others...

An elementary introduction to Hilbert modular forms, with a particular attention to their differential properties: Rankin-Cohen brakets, structure of differential rings... This text will appear in SMF Seminaires et Congres.

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…

These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.

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…

These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'' month at CIRM in 2004.

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

These are notes for a series of five lectures on "Moduli and degenerations of algebraic curves via tropical geometry" delivered at the CIMPA-CIMAT-ICTP School on Moduli of Curves, February 29-March 4, 2016 in Guanajuato, Mexico.

This is a survey paper based on a series of lectures given at the IHES in February/March 2015. In a first part, we recall the main results on the tempered holomorphic solutions of D-modules in the language of indsheaves and, as an…

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 overview contains 450 references of books, chapters of monographs, papers, preprints and Ph.~D.~thesises which are concerned with the theory and/or various applications of Hilbert C*-modules. To show a way through this amount of…