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2013 Postech Summer School in Number Theory
1. Multiple Dirichlet series(Gautam Chinta and Solomon Friedberg)
2. Overview of the Langlands functoriality conjecture (Chung Pang Mok)


  Date: July 5 (Friday) - July 11 (Thursday), 2013.

  Location: Math Build Room 404, Department of Mathematics, POSTECH, Pohang, South Korea.

  Organizers: YoungJu Choie (Postech), Jeehoon Park (Postech)

  Speakers: Gautam Chinta(CUNY), Solomon Friedberg(Boston College), Chung Pang Mok (McMaster University)


Registration

Lecture Schedule

Travel Information

Housing Information

Tips for POSTECH visitors


The following lecture series will be given.

The main speakers

Topics

Abstract

Gautam Chinta(CUNY),

Solomon Friedberg(Boston College)

A recent development on Multiple Dirichlet series

Lecture 1, 2, 5, 7, and 9 by Solomon Friedberg

Lecture 3, 4, 6, 8, and 10 by Gautam Chinta

 

Lecture 1: Eisenstein series and crystal graphs

Lecture 2: Kubota Dirichlet series

Lecture 3: Dynkin diagram heuristics

Lecture 4: Axiomatic method for constructing p-parts

Lecture 5: Metaplectic Eisenstein series: the n-fold cover of SL2

Lecture 6: function fields

Lecture 7: Higher rank Eisenstein series and their Whiattaker Fourier coefficients

Lecture 8: Periods of Eisenstein series

Lecture 9: Higher rank Eisenstein series and their Whiattaker Fourier coefficients

Lecture 10: Prehomogeneous vector spaces

Multiple Dirichlet Series are functions of several complex variables that mimic Langlands L-functions in that they posses meromorphic continuation and functional equation, but that are not Eulerian.

They arise in diverse way, including the study of automorphic forms on covers of groups, by means of deformations of the Weyl character formula, by attaching number-theoretic quantities to vertices of a crystal graph, by considering families of automorphic L-functions, and in the study of prehomogenous spaces.  

In this series of lectures, we will present an overview of this subject, starting from first principles and developing many aspects.

Chung Pang Mok(Mcmaster University)

Overview of the Langlands functoriality conjecture

(lecture notes can be downloaded)

Lecture 1: Introduction to the Langlands functoriality conjecture

Lecture 2: Automorphic L-functions

Lecture 3: Converse theorem

Lecture 4: Introduction to the trace formula

Lecture 5: The notion of endoscopy

Lecture 6: Trace formula and stabilization

Lecture 7: Introduction to Arthur's work on classical groups I

Lecture 8: Introduction to Arthur's work on classical groups II

Lecture 9: Introduction to Arthur's work on classical groups III

Lecture 10: Beyond Endoscopy?

The web of conjectures proposed by Langlands in the sixties, now collectively known as the Langlands' program, has been a unifying force in number theory and representation theory in the past two decades. In these lectures, we will give a selected overview of works on the Langlands functoriality conjecture.


If you have any inquiries regarding Postech Summer School 2013, please send e-mails to jinjwa@postech.ac.kr (Ju-A Jin, PMI Staff)


Last modified: July 16, 2013.