p-adic Aspects of Automorphic Forms

Spring School and International Conference

From April 22 to 29, 2017

IPM, Tehran, Iran

Organizers :

P. Kassaei (King’s College London)

F. Shahidi (Purdue Univ., USA)

J. Tilouine (Université Paris 13)

Mini-Courses (April 22-24)

P. Kassaei : Geometry of Hilbert Varieties and overconvergent modular forms (09:00-10:30)

V. Pilloni (CNRS, ENS Lyon) Weight one modular forms (11:00-12:30)

J. Tilouine : Algebraic Automorphic Forms, Hida Theory and the Eigenvariety (14:00-15:30)

Location: IPM, Niavaran Building, lecture hall 1

Conference (April 26-29)

P. Colmez (CNRS)

A. Conti (MPIM Bonn)

V. Hernandez (U. Paris 6)

P. Kassaei (King’s College London)

A.-C. Le Bras (ENS Paris)

S. Morel (Princeton U.)

M. Peche (ENS Lyon)

V. Pilloni (CNRS, ENS Lyon)

A. Skorobogatov (Imperial College, London)

B. Stroh (U. Paris 6)

J. Tilouine


Location: IPM, Niavaran Building






Introduction to the Arthur-Selberg trace formula and related techniques

Wen-Wei Li

Academy of Mathematics and Systems Science, Beijing

I will try to present the basic ideas and techniques for the Arthur-Selberg trace formula, which is an indispensable tool in Langlands program. If time permits, I will also talk about the geometric perspectives on the trace formula.

Time: Wed Aug 31 15:30-17:00 and Thu Sept. 1, 15:30-17:00

place: Niavaran Building



Esmail Arasteh Rad

(University of Münster )

March 14, 13:00-15:00.

Theory Of Local Model For The Moduli Of (G-)Shtukas
Abs. We discuss the theory of local models for  the moduli stacks of global Gshtukas, the function field analogs for Shimura varieties. Here G is a smooth affine group scheme over a smooth projective curve C. I wish to assume that the audiences have followed Sophie Morel’s lectures.

Place: Math Dept. Tarbiat Modares University.


Sophie Morel
(Princeton University)

March 10, 9-11 and 12:30-14:00

Cohomology of Shimura varieties


I will explain the conjectural 
description of the cohomology of a Shimura variety and how people have 
tried to prove this conjecture, on the example of a Siegel modular 3-fold. 
If time permits, I’ll also talk about the applications to the Langlands 
program for GL_n.

R=T theorems


I will explain what R and T stand for 
(ie universal deformation ring of Galois representations and ring of Hecke 
operators acting on a space of modular/automorphic forms), how to 
reformulate the Langlands correspondence as a R=T theorem, and why Vincent 
Lafforgue’s can be interpreted as the construction of a surjective map 

Place: IPM, Niavaran Building

Short Course

Sophie-MorelThe global Langlands correspondence over function fields, after Vincent Lafforgue

Sophie Morel
(Princeton University)

February 20-22,  2016

Abstract: I would like to explain what the global Langlands correspondence over function fields is, to present Vincent Lafforgue’s results about it and to give an idea of his methods. In the most famous case, that of the general linear group GL_n, Vincent Lafforgue recovers the results of his brother Laurent Lafforgue (and, for n=2, of Drinfeld), but there are in my opinion a few advantages to his methods:
– Even in this case, they are totally new and technically simpler.
– They work for general reductive groups, for example symplectic groups or orthogonal groups.
– They have been inspiring new ideas to approach the local Langlands correponsdance over local fields of any characteristic.

For registration click here

Algebraic Geometry Seminar (Talks Schedule)

Wed.13 Jan 
12:00-13:30 de Rham Cohomology (P. Bagherzadeh, F. Abbasy)
14:00-15:00 Hodge Structures (M. Najafpour, M. Akrami)
15:30-16:30 Infinitesimal Criterion For Etalness/Smoothness (?,?) 
17:00-18:15 Schlessinger’s Theorem (S. Tayebi) 

Thu. 14 Jan 
08:45-09:45 Bezout’s Theorem (F. Kamankesh) 
10:00-11:00 Intersection Theory On Surfaces (K. Amini, R. Mahkam) 

12:30-13:30 Riemann-Roch and Riemann-Hurwitz Theorems (M. Jadidi, Z. Kochakzadeh) 
14:00-15:00    Algebraic Fundamental Group (A. Cheraghi, F. Taheri)
15:15-16:15 Zariski’s Main Theorem (S. Gholami, T. Torkaman)

Wed Jan 27
12:00-13:30 Chow Ring (M. Fard) 
15:30-16:30 Leray-Hirsch Theorem For Chow Rings (B. Khazaie) 
16:45-18:00 GAGA (F. Huseini, M. Rezaeian) 

Thu. 28 Jan
08:45-09:45 Bertini’s Theorem (A. Akhavan, A. Soofiani) 
10:00-11:00 Embedding of Curves in P^3 (M.Fashami) 

Wed. 3 Feb 
10:00-11:00 Jacobian Of Curves (E. Shahhoseini, D. Khajehpour)

15:30-16:30 Vector Bundles Over Projective Line (R. Khorram Pajouh,S. Sharifi) 
16:45-17:45: Vector Bundles Over Elliptic Curves (F. Amiri)

Second Semester Courses

Iwasawa Theory

Dr. R. Taleb

Course Description: Iwasawa theory concerns the growth of the arithmetic objects, e.g. class groups, elliptic curves, abelian variety, motives, etc., over infinite towers of number fields. The aim of this course is an introduction to the basic concepts and ideas of this theory, mainly in the class group case and – if time permits – in the elliptic curve case. More precisely, we intend to describe some algebraic concepts, e.g. Iwasawa modules and some Galois groups as their examples, and also some important theorems and conjectures, e.g. Iwasawa theorem on the growth of class numbers, Leopoldt’s conjecture, µ- invariant conjecture, Greenberg conjecture, in this theory. Then, after explaining the fundamental analytic objects of this theory, i.e. p-adic L-functions attached to number fields, we can formulate the main conjecture of Iwasawa theory and discuss about it. Having some background on algebraic number theory would be helpful for this course. However, we try to make a short review of necessary tools in the first one or two sessions.

Place: Math. Dept., Shahid Beheshti Univ.
Date and Time: Wednesdays 09:00-10:45

Modular Forms

Dr. K. Monsef

Place: Math. Dept., Shahid Beheshti Univ.
Date and Time: Wednesdays 11:00-13:00
Elliptic Curves
Dr. Rajaei and Dr. Setayesh
Place: Math department, Tarbiat Modares University
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Representation Theory Of Algebraic

Dr. A. Jafari

Place: IPM, Niavaran Building

Date and Time: Thursdays, 09:00-10:30 and 12:30-14:00