Aug 18, 2014
Monday

09:15 AM  09:30 AM


Welcome

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


GrossZagier formula: why is it right
ShouWu Zhang (Princeton University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
Heegner points and the original GrossZagier formula
MordellWeil Theorem, Modularity of elliptic curves, Heegner points,
and (orginal) GrossZagier formula
 Supplements


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


An examplebased introduction to Shimura varieties and their compactifications
KaiWen Lan (University of Minnesota, Twin Cities)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
I will introduce various examples of Shimura varieties, and explain what some important classes of their compactifications are like. I will begin with complex coordinates, but when good theories of their integral models are available, I will also explain what they are like. The lectures will be for people who are not already familiar with these topicsfor most of them, some willingness to see matrices larger than 2x2 ones should suffice. (I hope to allow simple factors of all possible types A, B, C, D, and E to show up if time permits. Nevertheless, it is not necessary to know beforehand what this means.)
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Construction of some modular symbols
Birgit Speh (Cornell University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Analytic continuation of padic modular forms and applications to modularity
Payman Kassaei (McGill University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
The lecture series will start with a brief introduction to rigid analytic geometry. I will then introduce modular curves from various viewpoints (complex analytic, algebraic, and padic analytic) and use them to give a geometric definition of padic and overconvergent modular forms and Hecke operators. I will next show how to use the padic geometry of the modular curves towards padic analytic continuation of overconvergent modular forms. Finally, I will demonstrate an application of these results to modularity of certain Galois representations which can itself be used to prove certain cases of the Artin conjecture. If time allows, I would explain briefly how these ideas extend to higher dimensions by illustrating the easier case of Hilbert modular surfaces.
 Supplements



Aug 19, 2014
Tuesday

09:30 AM  10:30 AM


GrossZagier formula: why is it right?
ShouWu Zhang (Princeton University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
Waldspurger formula and GrossZagier formulae on Shimura curves
Waldspurer formula, GrossZagier formula for Shimura curves, padic
Waldspurger and padic GrossZagier
 Supplements


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


An examplebased introduction to Shimura varieties and their compactifications
KaiWen Lan (University of Minnesota, Twin Cities)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
I will introduce various examples of Shimura varieties, and explain what some important classes of their compactifications are like. I will begin with complex coordinates, but when good theories of their integral models are available, I will also explain what they are like. The lectures will be for people who are not already familiar with these topicsfor most of them, some willingness to see matrices larger than 2x2 ones should suffice. (I hope to allow simple factors of all possible types A, B, C, D, and E to show up if time permits. Nevertheless, it is not necessary to know beforehand what this means.)
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Construction of some modular symbols
Birgit Speh (Cornell University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
 
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Analytic continuation of padic modular forms and applications to modularity
Payman Kassaei (McGill University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
The lecture series will start with a brief introduction to rigid analytic geometry. I will then introduce modular curves from various viewpoints (complex analytic, algebraic, and padic analytic) and use them to give a geometric definition of padic and overconvergent modular forms and Hecke operators. I will next show how to use the padic geometry of the modular curves towards padic analytic continuation of overconvergent modular forms. Finally, I will demonstrate an application of these results to modularity of certain Galois representations which can itself be used to prove certain cases of the Artin conjecture. If time allows, I would explain briefly how these ideas extend to higher dimensions by illustrating the easier case of Hilbert modular surfaces.
 Supplements


04:30 PM  06:20 PM


Reception

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements




Aug 20, 2014
Wednesday

09:00 AM  10:00 AM


GrossZagier formula: why is it right?
ShouWu Zhang (Princeton University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
GanGrossPrasad conejcture
GanGrossPrasad conjeture for unitary groups, relative trace
formula and fundamental lemma, arithmetic analogues.
 Supplements


10:00 AM  10:30 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



10:30 AM  11:30 AM


An examplebased introduction to Shimura varieties and their compactifications
KaiWen Lan (University of Minnesota, Twin Cities)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
I will introduce various examples of Shimura varieties, and explain what some important classes of their compactifications are like. I will begin with complex coordinates, but when good theories of their integral models are available, I will also explain what they are like. The lectures will be for people who are not already familiar with these topicsfor most of them, some willingness to see matrices larger than 2x2 ones should suffice. (I hope to allow simple factors of all possible types A, B, C, D, and E to show up if time permits. Nevertheless, it is not necessary to know beforehand what this means.)
 Supplements


11:30 AM  12:30 PM


Aspects of the mod p representation theory of padic reductive groups
Rachel Ollivier (University of British Columbia)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
These lectures will focus on the mod p representation theory of a split padic reductive group G, using GL(2) as a running example. We hope to emphasize the differences between the mod p and complex representations of G while keeping in mind that the theory is partly motivated by the mod p and complex local Langlands programs.
We will start with remarks regarding finite reductive groups. We will then compare the homological properties of certain categories of mod p and complex representations of G (and the associated propIwahori Hecke algebra). In particular, in the complex setting, the theory of coefficient systems on the BruhatTits building by Schneider and Stuhler gives a way to construct explicit projective resolutions. We will explore what remains from this theory in the mod p setting. This will help us describe the first step in the construction of Colmez' functor yielding the mod p local Langlands correspondence for GL(2,Q_p).
 Supplements



Aug 21, 2014
Thursday

09:30 AM  10:30 AM


Cohomology of Arithmetic Groups
Frank Calegari (Northwestern University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
We discuss some basic techniques for studying the arithmetic aspects of the cohomology of arithmetic groups. In contrast to the lectures of Speh, we shall focus on cohomology with coefficients over the integers or over finite fields rather than over the real numbers.
 Supplements


10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Aspects of the mod p representation theory of padic reductive groups
Rachel Ollivier (University of British Columbia)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
These lectures will focus on the mod p representation theory of a split padic reductive group G, using GL(2) as a running example. We hope to emphasize the differences between the mod p and complex representations of G while keeping in mind that the theory is partly motivated by the mod p and complex local Langlands programs.
We will start with remarks regarding finite reductive groups. We will then compare the homological properties of certain categories of mod p and complex representations of G (and the associated propIwahori Hecke algebra). In particular, in the complex setting, the theory of coefficient systems on the BruhatTits building by Schneider and Stuhler gives a way to construct explicit projective resolutions. We will explore what remains from this theory in the mod p setting. This will help us describe the first step in the construction of Colmez' functor yielding the mod p local Langlands correspondence for GL(2,Q_p).
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


An overview of the theory of padic Galois representations
Jared Weinstein (Boston University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
We give an introductory discussion of the theory of padic representations of the field of padic numbers. Topics will include: Tate's pdivisible groups paper, the field of norms, the formalism of period rings, and (phi,Gamma)modules
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Phigamma modules and padic Hodge theory
Gabriel Dospinescu (École Normale Supérieure de Lyon)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
This series of lectures, which build on Jared Weinstein's talks, will be a light introduction to the theory of phigamma modules and their interactions with padic Hodge theory. We will discuss Fontaine's equivalence of categories, give examples of phigamma modules and present Berger's fundamental results which link phigamma modules and padic Hodge theory. Depending on time, we may say a few words about the applications of phigamma modules to Galois cohomology and to the padic Langlands correspondence for GL_2(Q_p).
 Supplements




Aug 22, 2014
Friday

09:30 AM  10:30 AM


TBA

 Location
 MSRI: Simons Auditorium
 Video


 Abstract
 
 Supplements



10:30 AM  11:00 AM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Cohomology of Arithmetic Groups
Frank Calegari (Northwestern University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
We discuss some basic techniques for studying the arithmetic aspects of the cohomology of arithmetic groups. In contrast to the lectures of Speh, we shall focus on cohomology with coefficients over the integers or over finite fields rather than over the real numbers.
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


An overview of the theory of padic Galois representations
Jared Weinstein (Boston University)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
We give an introductory discussion of the theory of padic representations of the field of padic numbers. Topics will include: Tate's pdivisible groups paper, the field of norms, the formalism of period rings, and (phi,Gamma)modules
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 MSRI: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Phigamma modules and padic Hodge theory
Gabriel Dospinescu (École Normale Supérieure de Lyon)

 Location
 MSRI: Simons Auditorium
 Video

 Abstract
This series of lectures, which build on Jared Weinstein's talks, will be a light introduction to the theory of phigamma modules and their interactions with padic Hodge theory. We will discuss Fontaine's equivalence of categories, give examples of phigamma modules and present Berger's fundamental results which link phigamma modules and padic Hodge theory. Depending on time, we may say a few words about the applications of phigamma modules to Galois cohomology and to the padic Langlands correspondence for GL_2(Q_p).
 Supplements


