

2013 Postech Summer School in Number Theory 
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
pparts Lecture 5: Metaplectic Eisenstein series: the
nfold 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 Lfunctions 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
numbertheoretic quantities to vertices of a crystal graph, by considering
families of automorphic Lfunctions, 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 Lfunctions 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 emails to jinjwa@postech.ac.kr (JuA Jin, PMI
Staff)
Last modified: July 16, 2013.