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Summer Graduate School

New Geometric Techniques in Number Theory July 01, 2013 - July 12, 2013
Parent Program: New Geometric Methods in Number Theory and Automorphic Forms
Location: MSRI: Simons Auditorium
Organizers Toby Gee (Imperial College, London), LEAD Ariane Mézard (L'Institut de Mathématiques de Jussieu), David Nadler (University of California, Berkeley), Peter Scholze (Universität Bonn)
Lecturer(s) No Lecturers Assigned Yet.
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Description

The branches of number theory most directly related to automorphic forms have seen enormous progress over the past five years.  Techniques introduced since 2008 have made it possible to prove many new arithmetic applications. The purpose of the current workshop is to drow the attention of young students or researchers to new questions that have arisen in the course of bringing several chapters in the Langlands program and related algebraic number theory to a close. We will focus especially on some precise questions of a geometric nature, or whose solutions seem to require new geometric insights.  A graduate level in Number Theory is expected.

This two-week workshop will be devoted to the following subjects: Automorphy lifting theorems, p-adic local Langlands program, Characters of categorical representations and Hasse-Weil zeta function. During the first week, the lecturers present an open question and related mathematical objects. The first  exercice  sessions serve to direct the participants to an appropriate subject depending on their level. During the second week, the lecturers give some more advanced lectures on the field.

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Schedule
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Jul 01, 2013
Monday
09:00 AM - 09:15 AM
  Welcome
09:15 AM - 10:45 AM
  Lecture
David Nadler (University of California, Berkeley)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Lecture
Ariane Mézard (L'Institut de Mathématiques de Jussieu)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
Peter Scholze (Universität Bonn)
02:45 PM - 03:15 PM
  Asymptotic behaviors of higher Mahler Measure
Arunabha Biswas (Texas Tech University)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
Gabriel Dospinescu (École Normale Supérieure de Lyon)
Jul 02, 2013
Tuesday
09:15 AM - 10:45 AM
  Lecture
Ariane Mézard (L'Institut de Mathématiques de Jussieu)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Penghui Li (University of California, Berkeley)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
David Nadler (University of California, Berkeley)
02:45 PM - 03:15 PM
  Representations and Pseudorepresentations
Carl Wang Erickson (Brandeis University)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
Timo Richarz (Max-Planck-Institut für Mathematik)
Jul 03, 2013
Wednesday
09:15 AM - 10:45 AM
  Lecture
Peter Scholze (Universität Bonn)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 01:45 PM
  BBQ
01:45 PM - 02:45 PM
  Problem Session
Gabriel Dospinescu (École Normale Supérieure de Lyon)
02:45 PM - 03:45 PM
  Problem Session
Timo Richarz (Max-Planck-Institut für Mathematik)
03:45 PM - 04:45 PM
  Problem Session
Penghui Li (University of California, Berkeley)
Jul 05, 2013
Friday
09:15 AM - 10:45 AM
  Lecture
David Nadler (University of California, Berkeley)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Lecture
Peter Scholze (Universität Bonn)
12:45 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
Ariane Mézard (L'Institut de Mathématiques de Jussieu)
02:45 PM - 03:15 PM
  Selmer groups and class groups
Kestutis Cesnavicius (Massachusetts Institute of Technology)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
Penghui Li (University of California, Berkeley)
Jul 08, 2013
Monday
09:15 AM - 10:45 AM
  Lecture
Toby Gee (Imperial College, London)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Gabriel Dospinescu (École Normale Supérieure de Lyon)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
David Nadler (University of California, Berkeley)
02:45 PM - 03:15 PM
  Towards a Langlands correspondence for Hecke modules of SL_n in characteristic p
Karol Koziol (Columbia University)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
George Boxer (Harvard University)
Jul 09, 2013
Tuesday
09:15 AM - 10:45 AM
  Lecture
Ariane Mézard (L'Institut de Mathématiques de Jussieu)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Timo Richarz (Max-Planck-Institut für Mathematik)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
Toby Gee (Imperial College, London)
02:45 PM - 03:15 PM
  p-adic functoriality
Judith Ludwig (Imperial College, London)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
George Boxer (Harvard University)
Jul 10, 2013
Wednesday
09:15 AM - 10:45 AM
  Lecture
Peter Scholze (Universität Bonn)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Gabriel Dospinescu (École Normale Supérieure de Lyon)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Lecture
Toby Gee (Imperial College, London)
02:45 PM - 03:15 PM
  On images of Galois representations associated to non-CM Hida families of modular forms
Jaclyn Lang (University of California, Los Angeles)
03:15 PM - 03:45 PM
  Local constants for families of representations of GL(2) of a local field
Gilbert Moss (University of Texas)
03:45 PM - 04:45 PM
  Problem Session
George Boxer (Harvard University)
Jul 11, 2013
Thursday
09:15 AM - 10:45 AM
  Lecture
Toby Gee (Imperial College, London)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Timo Richarz (Max-Planck-Institut für Mathematik)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Problem Session
Gabriel Dospinescu (École Normale Supérieure de Lyon)
01:45 PM - 02:45 PM
  Problem Session
Penghui Li (University of California, Berkeley)
02:45 PM - 03:15 PM
  Interpolating Periods
Shrenik Shah (Princeton University)
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Problem Session
George Boxer (Harvard University)
Jul 12, 2013
Friday
09:15 AM - 10:45 AM
  Problem Session
Peter Scholze (Universität Bonn)
09:15 AM - 10:45 AM
  Problem Session
Timo Richarz (Max-Planck-Institut für Mathematik)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:15 PM
  Problem Session
Penghui Li (University of California, Berkeley)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 02:45 PM
  Group Presentation
02:45 PM - 03:15 PM
  Group Presentation
03:15 PM - 03:45 PM
  Tea Break
03:45 PM - 04:45 PM
  Group Presentation