Timetable


25(Tue) Room : Main Conference Room (Dai Kaigi Shitsu)
9:30-10:30 10:30-11:30 12:00-13:00 14:30-15:30 16:00-17:00 17:15-18:15
Registration (*) Shim (*) STF Taniguchi Yamamoto Nicole
26(Wed) Room : Main Conference Room (Dai Kaigi Shitsu)
9:30-10:30 10:45-11:45 12:00-13:00 14:30-15:30 16:00-17:00 17:15-18:15 19:00-
(*) Gal (*) Rep1 Dat (TBA) Gee Mieda Banquet
27(Thu) Room : Main Conference Room (Dai Kaigi Shitsu)
9:30-10:30 10:45-11:45 12:00-13:00 14:30-15:30 16:00-17:00 17:15-18:15
(*) Rep2 Orlik Lan Stroh Barnet-Lamb Pottharst
28(Fri) Room : Main Conference Room (Dai Kaigi Shitsu)
9:30-10:30 10:45-11:45 12:00-13:00 14:30-15:30 16:00-17:00
Herzig Imai Ito Yoshida Shin
29(Sat) Free / Excursion (optional)

(*) : Introductory lectures for students and non-specialists
(Shim) Introduction to Shimura varieties
(STF) Stable trace formula, Base change for unitary groups
(Gal) mod p Galois representations, Serre weights, modularity
(Rep) p-adic representation theory, locally analytic representations

Program


(*) : Introductory lectures for students and non-specialists
Nov 25 (Tue)
Room : Main Conference Room (Dai Kaigi Shitsu)
9:30 - 10:30 Registration
10:30 - 11:30Tetsushi Ito (Kyoto University)
(*) Introduction to Shimura varieties
[Abstract], [Handwritten Notes], [Webpage of the speaker]
12:00 - 13:00Sug Woo Shin (University of Chicago/Institute for Advanced Study)
(*) Base change for unitary groups
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Lunch
14:30 - 15:30Takashi Taniguchi (Kobe University)
Exceptional groups and Sato-Shintani's zeta functions
[Abstract], [Handwritten Notes]
Coffee/Tea
16:00 - 17:00Shuji Yamamoto (University of Tokyo)
On Shintani's ray class invariant for totally real number fields
[Abstract], [Handwritten Notes]
17:15 - 18:15 Marc-Hubert Nicole (Paris 7)
Purity of level m stratifications
[Abstract], [Handwritten Notes], [Webpage of the speaker], [Slides (RIMS, Dec, 2008)]
Nov 26 (Wed)
Room : Main Conference Room (Dai Kaigi Shitsu)
9:30 - 10:30Florian Herzig (Northwestern University)
(*) Generalisations of Serre's conjecture for GL_n
[Abstract], [Handwritten Notes], [Webpage of the speaker]
10:45 - 11:45Matthias Strauch (Indiana University)
(*) Locally analytic representations
[Abstract], [Handwritten Notes]
12:00 - 13:00Jean-Francois Dat (Paris 6)
Looking for a geometric construction of (modular) local Langlands' correspondence
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Lunch
14:30 - 15:30(TBA)
(TBA)
Coffee/Tea
16:00 - 17:00Toby Gee (Harvard University)
The conjectural connections between Galois representations and automorphic representations
[Abstract], [Handwritten Notes], [Webpage of the speaker]
17:15 - 18:15Yoichi Mieda (Kyushu University)
On Lefschetz trace formula for adic spaces
[Abstract], [Handwritten Notes]
19:00 -Banquet
Nov 27 (Thu)
Room : Main Conference Room (Dai Kaigi Shitsu)
9:30 - 10:30 Matthias Strauch (Indiana University)
(*) Parabolically induced representations
[Abstract], [Handwritten Notes]
10:45 - 11:45 Sascha Orlik (Bonn)
Equivariant vector bundles on p-adic period spaces
[Abstract], [Handwritten Notes], [Webpage of the speaker]
12:00 - 13:00 Kai-Wen Lan (Princeton University)
Extensions over toroidal boundaries of Shimura varieties
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Lunch
14:30 - 15:30 Benoit Stroh (Nancy University, Institut Elie Cartan)
Compactification of Shimura varieties at some bad reduction places
[Abstract], [Handwritten Notes]
Coffee/Tea
16:00 - 17:00 Thomas Barnet-Lamb (Harvard University)
Potential automorphy for certain Galois representations to GL(n)
[Abstract], [Handwritten Notes], [Webpage of the speaker]
17:15 - 18:15Jonathan Pottharst (Boston College)
Selmer groups over eigenvarieties
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Nov 28 (Fri)
Room : Main Conference Room (Dai Kaigi Shitsu)
9:30 - 10:30Florian Herzig (Northwestern University)
Weight cycling and Serre-type conjectures
[Abstract], [Handwritten Notes], [Webpage of the speaker]
10:45 - 11:45 Naoki Imai (University of Tokyo)
On the connected components of moduli spaces of finite flat models
[Abstract], [Handwritten Notes]
12:00 - 13:00 Tetsushi Ito (Kyoto University)
Construction of Galois representations I - The fundamental lemma (after Laumon-Ngo)
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Lunch
14:30 - 15:30Teruyoshi Yoshida (Harvard University/University of Cambridge)
Construction of Galois representations II - Geometry of Shimura Varieties
[Abstract], [Handwritten Notes], [Webpage of the speaker]
Coffee/Tea
16:00 - 17:00Sug Woo Shin (University of Chicago/Institute for Advanced Study)
Construction of Galois representations III - Comparison with Trace Formulas
[Abstract], [Handwritten Notes], [Webpage of the speaker]

Abstract


Speaker: Thomas Barnet-Lamb (Harvard)
Title: Potential automorphy for certain Galois representations to GL(n)
Abstract: I will describe a recent generalization of mine to a theorem of Harris, Shepherd-Barron, and Taylor, showing that have certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field. The main innovation is that the result applies to Galois representations to $\GL_n$, where the previous work dealt with representations to $\Sp_n$; I can also dispense with certain congruence conditions which existed in teh earlier work. The main technique is the consideration of the cohomology the Dwork hypersurface, and in particular, of pieces of this cohomology other than the invariants under the natural group action.

Speaker: Jean-Francois Dat (Paris 6)
Title: Looking for a geometric construction of (modular) local Langlands' correspondence
Abstract: The l-adic or complex local Langlands correspondence is characterized by matching of L-functions and epsilon factors. Vigneras has established a Langlands-type correspondence for mod l representations. Although L-functions and epsilon factors have been defined for such representations, they are too coarse invariants for the purpose of characterizing such a correspondence. In this talk we will propose a conjectural geometric-cohomological realization of the composition of this correspondence with Zelevinski's involution, using a Lefschetz operator on the cohomology of the "twin towers".

Speaker: Toby Gee (Harvard University)
Title: The conjectural connections between Galois representations and automorphic representations
Abstract: We discuss joint work with Kevin Buzzard, formulating precise conjectures on the relationships between between Galois representations and automorphic representations for arbitrary connected reductive groups.

Speaker: Florian Herzig (Northwestern University)
Title: Generalisations of Serre's conjecture for GL_n
Abstract: Serre's Conjecture on the modularity of odd, two-dimensional mod p Galois representations was recently established by Khare-Wintenberger and Kisin. We will discuss generalisations of Serre's Conjecture to higher-dimensional Galois representations rho, with special emphasis on the possible (Serre) weights in which rho can occur.

Speaker: Florian Herzig (Northwestern University)
Title: Weight cycling and Serre-type conjectures
Abstract: Suppose that rho is a three-dimensional modular mod p Galois representation whose restriction to the decomposition groups at p is irreducible and generic. If rho is modular in some (Serre) weight, then a representation-theoretic argument shows that it also has to be modular in certain other weights (we can give a short list of possibilities). This goes back to an observation of Buzzard for GL_2. Previously we formulated a Serre-type conjecture on the possible weights of rho. Under the assumption that the weights of rho are contained in the predicted weight set, we apply the above weight cycling argument to show that rho is modular in precisely all the nine predicted weights. This is joint work with Matthew Emerton and Toby Gee.

Speaker: Tetsushi Ito (Kyoto University)
Title: Introduction to Shimura varieties
Abstract: ...

Speaker: Tetsushi Ito (Kyoto University)
Title: Construction of Galois representations I - The fundamental lemma (after Laumon-Ngo)
Abstract: .....

Speaker: Naoki Imai (University of Tokyo)
Title: On the connected components of moduli spaces of finite flat models
Abstract: Recently, Kisin made a way to get information of a deformation ring of a local Galois representation from a moduli space of finite flat group schemes. He conjectured that the non-ordinary component of the moduli space is connected, and proved this conjecture for special p-adic fields. In this talk, we prove the conjecture for general p-adic fields. As an application, we can prove a theorem comparing a deformation ring and a Hecke ring.

Speaker: Kai-Wen Lan (Princeton University)
Title: Extensions over toroidal boundaries of Shimura varieties
Abstract: We will explain how to construct systematically "good" extensions of objects such as automorphic bundles, products of universal families, Hecke correspondences, etc over the boundaries of toroidal compactifications of smooth integral models of PEL-type Shimura varieties.

Speaker: Yoichi Mieda (Kyushu University)
Title: On Lefschetz trace formula for adic spaces
Abstract: Recall that the notion of adic spaces, due to Roland Huber, is one of the modern formulations of rigid analytic spaces. We will discuss on the Lefschetz trace formula for quasi-compact adic spaces over a non-archimedean field. If an adic space is not proper, the formula should be much more complicated than that for a scheme which is not proper. In this talk, we will explain why such difference appears, and give a positive result in a special case.

Speaker: Marc-Hubert Nicole (Paris 7)
Title: Purity of level m stratifications
Abstract: We will discuss stratifications coming from truncations of Barsotti-Tate groups (also called p-divisible groups), generalizing the Ekedahl-Oort stratification. We will recall some background material about stratifications, explain the hierarchy of purity properties, and describe in detail the situation for level m stratifications. We will illustrate the main result in the case of the Siegel modular varieties, and mention how our techniques apply to good reductions of Shimura varieties of Hodge type. Joint work with A. Vasiu and T. Wedhorn.

Speaker: Sascha Orlik (Universitaet Bonn)
Title: Equivariant vector bundles on p-adic period spaces
Abstract: Let X be Drinfeld's half space of dimension d over a p-adic field K, i.e. the complement of all K-rational hyperplanes in projective space P^d. In this talk we construct for every homogenous vector bundle F on P^d, a GL_{d+1}(K)-equivariant filtration by closed subspaces on the K-Frechet H^0(X,F). This gives rise by duality to a filtration by locally analytic GL_{d+1}(K)-representations on the strong dual H^0(X,F)'. We determine the graded pieces of this filtration as locally analytic representations. This generalises a previous work of Schneider and Teitelbaum who considered the case of the canonical bundle. If there will be time left at the end, I will sketch how to generalise this construction to arbitrary p-adic period spaces.

Speaker: Jonathan Pottharst (Boston College)
Title: Selmer groups over eigenvarieties
Abstract: Greenberg defined Selmer groups over p-adic deformations of motives that are "ordinary". This leaves open the question of how to define a Selmer group over, for example, the eigencurve of Coleman-Mazur. We present a conjectural program to do this, using a direct generalization of Greenberg's hypothesis in the setting of (phi,Gamma)-modules, and give evidence by comparing our local conditions to Bloch-Kato's.

Speaker: Sug Woo Shin (University of Chicago/Institute for Advanced Study)
Title: Base change for unitary groups
Abstract: We are interested in the quadratic base change from automorphic representations of unitary groups to those of general linear groups. For one thing, it helps to understand (or classify) the automorphic representations of unitary groups. Another point is that this base change is important in analyzing the cohomology of PEL Shimura varieties of unitary type. Following the ideas by Clozel, Harris and Labesse, we explain how to use the stable trace formula and the twisted trace formula to establish base change results in many cases.

Speaker: Sug Woo Shin (University of Chicago/Institute for Advanced Study)
Title: Construction of Galois representations III - Comparison with Trace Formulas
Abstract: We report a recent result, due to Clozel-Harris-Labesse, Morel and the speaker, extending the previous work of Clozel, Kottwitz, Harris-Taylor and Taylor-Yoshida.
There are two main features in our work. One feature, which is also crucial in the other improvements, is the use of the stable trace formula, which became available unconditionally after Ngo (extending Laumon-Ngo) finished the proof of the fundamental lemma. The other feature, which is unique in our approach, is the extension of Harris-Taylor's method to endoscopic setting. The key is a general version of the counting point formula for Igusa varieties and its stabilization.

Speaker: Matthias Strauch (Indiana University)
Title: Locally analytic representations
Abstract: In this talk we will define what a locally analytic representation is, and we will discuss the basic notions from non-Archimedean functional analysis underlying this concept, as well as examples. Whereas in the classical theory of smooth representations a p-adic reductive group G is merely considered as a topological group, the starting point of the theory of locally analytic representations is to consider G as a group object in the category of locally analytic manifolds. Therefore, if we are given an action of G on a topological vector space V, we may ask, for every vector v in V, if the orbit map G -> V, g \mapsto gv, is a locally analytic map on the group G, i.e., if it has a convergent power series expansion in a neighborhood of the unit element of G. This is the central condition on the representation V to be locally analytic. Then we will discuss distribution algebras (which play a role which is analogous to the role of Hecke algebras in the theory of smooth representations). The distribution algebras are then used to introduce admissibility conditions on locally analytic representations.

Speaker: Matthias Strauch (Indiana University)
Title: Parabolically induced representations
Abstract: In this talk we will study in detail an important class of locally analytic representations, namely those which come from (finite-dimensional) locally analytic representations of Levi subgroups via parabolic induction. We will show how the topological dual space of such an induced representation relates to a generalized Verma module. This will lead us to investigate the relation between certain completions of the distribution algebra and (the closures of) universal enveloping algebras. From this we deduce that the induced representation is topologically irreducible if the generalized Verma module is irreducible. (A result that was first proved for split groups over Q_p by Frommer.) We also plan to say something about the reducible case and Jordan-Hoelder series, and the case where the representation of the Levi subgroup is infinite-dimensional.

Speaker: Benoit Stroh (Nancy University, Institut Elie Cartan)
Title: Compactification of Shimura varieties at some bad reduction places
Abstract: A natural problem in algebraic geometry is to compactify Shimura varieties. In 1975, Ash, Mumford, Rapoport, and Tai constructed toroidal compactifications of such varieties over the complex numbers. Thanks to the work of Faltings and Chai in 1990 and its generalization by Lan in 2008, we know that these compactifications extend to the set of primes of good reduction when the Shimura variety is of PEL type. In this talk, we will explain how such compactifications extend to some bad reduction places corresponding to parahoric level structures.

Speaker: Takashi Taniguchi (Kobe University)
Title: Exceptional groups and Sato-Shintani's zeta functions
Abstract: The notion of prehomogenoues vector space and its zeta function is founded by Mikio Sato and Takuro Shintani. Some of them, in particular related to nilpotent orbits of exceptional groups, have interesting arithmetic structures. In this talk, we will study these objects over a general number field and discuss possible applications to number theory of exceptional groups.

Speaker: Shuji Yamamoto (University of Tokyo)
Title: On Shintani's ray class invariant for totally real number fields
Abstract:For a ray class $C$ of a totally real number field of degree $n$, we define a real number $X(C)$ by combining the first derivative of the partial zeta function. It was first introduced by Shintani in the case of a real quadratic field. It can be expressed by special values of the multiple sine function, and has a canonical factorization $X=X_1\cdots X_n$, where each factor $X_i=X_i(C)$ represents the contribution of a real place. We also show how $X_i$ behaves when the signature of $C$ at a real place is changed.

Speaker: Teruyoshi Yoshida (Harvard University/University of Cambridge)
Title: Construction of Galois representations II - Geometry of Shimura Varieties
Abstract: As a preliminary to Shin's talk on construction of Galois representations, we explain the basic ingredients that go into the computation of the cohomology of Shimura varieties of (generalized) Harris-Taylor type. We cover the definition and geometry of such Shimura varieties, where Drinfeld's theory of defomation and level structures on 1-dimensional Barsotti-Tate groups plays the key role. We will define the Rapoport-Zink spaces and Igusa varieties occuring in this case, and discuss the so-called "first identity" and "Mantovan functors".


Last modified : December 3, 2008