Dec 01, 2014
Monday
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09:15 AM - 09:30 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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09:30 AM - 10:30 AM
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Parabolically induced mod p representations of reductive p-adic groups
Marie-France Vigneras (Université de Paris VII (Denis Diderot))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:00 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Moduli stacks of local Galois representations
Matthew Emerton (University of Chicago)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Integral p-adic Hodge theory
Peter Scholze (Universität Bonn)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
We will discuss joint work with Bhargav Bhatt and Matthew Morrow which proves a comparison between integral p-adic etale cohomology and integral crystalline cohomology, using a geometric construction of Breuil-Kisin modules.
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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04:10 PM - 05:00 PM
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MSRI/Evans Lecture
Pierre Colmez (Institut de Mathématiques de Jussieu)
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- Location
- 740 Evans Hall, UC Berkeley
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Dec 02, 2014
Tuesday
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09:30 AM - 10:30 AM
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Special parahorics and exotic good reduction
Wei Zhang (Massachusetts Institute of Technology)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will report on joint work with M. Rapoport and B. Smithling, on an "arithmetic transfer conjecture" (ATC). Similar to the arithmetic fundamental lemma conjecture (for unramified unitary groups over a p-adic field), the transfer conjecture connects the derivative of a relative orbital integral to an intersection number on a formal moduli space of $p$-divisible groups associated to a special parahoric of a ramified unitary group. Miraculously, this formal moduli space has good reduction.
- Supplements
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10:30 AM - 11:00 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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Cycles on Shimura varieties and applications to Faltings heights
Benjamin Howard (Boston College)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I'll speak about ongoing joint work with Bruinier, Kudla, Rapoport, and Yang on the modularity of certain generating series of cycles on unitary Shimura varieties, and applications to new cases of Colmez's conjecture on the Faltings heights of CM abelian varieties.
- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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On the Hodge-Tate period map for Shimura varieties of Hodge type
Ana Caraiani (Imperial College, London)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G(A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G(Q_p) and can be thought of as a p-adic analogue of the Borel embedding. In this talk, I will describe a canonical construction of the Hodge-Tate period map and of automorphic vector bundles for Shimura varieties of Hodge type. This is part of ongoing joint work with Peter Scholze.
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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Higher Koecher's principle
Kai-Wen Lan (University of Minnesota, Twin Cities)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I will report on a generalization of the classical Koecher's principle for the coherent cohomology of Shimura varieties.
- Supplements
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04:30 PM - 05:00 PM
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Poster Session
Mladen Dimitrov (Université de Lille I (Sciences et Techniques de Lille Flandres Artois)), Volker Heiermann (Université d'Aix-Marseille (AMU)), Valentin Hernandez (Polytechnical University of Cataluña (Barcelona)), Jean-Pierre Labesse (Centre International de Recontres Mathématiques (CIRM), Luminy), Arthur-César Le Bras (Rheinische Friedrich-Wilhelms-Universität Bonn), Jie LIN (Université de Paris VII (Denis Diderot)), Marc-Hubert Nicole (Université de Caen)
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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05:00 PM - 09:00 PM
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Banquet at Hong Kong East Ocean Seafood Restaurant
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- Location
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Dec 03, 2014
Wednesday
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09:00 AM - 10:00 AM
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Special Values of automorphic L-functions and congruences
A. Raghuram (Indian Institute of Science Education and Research)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Hida proved in 1981 that if a prime p divides the algebraic part of the value at s = 1 of the adjoint L-function of a holomorphic cusp form f, then there is another cusp form g such that f is congruent to g modulo the prime p. This result was generalized to Hilbert modular forms by Eknath Ghate and Mladen Dimitrov, and to certain cusp forms on GL(2) over an imaginary quadratic field by Eric Urban, and recently to cusp forms on GL(2) over any number field by Namikawa. In this talk, I will discuss further generalizations of this phenomenon to the context adjoint L-values for cohomological cuspidal automorphic representations of GL(n) over any number field. This is joint work with Baskar Balasubramanyam
- Supplements
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10:00 AM - 10:30 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:30 AM
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The exterior algebra in the cohomology of an arithmetic group
Akshay Venkatesh (Institute for Advanced Study)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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11:30 AM - 12:00 PM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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12:00 PM - 01:00 PM
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Branching laws and period integrals for non-tempered representations.
Dipendra Prasad (Tata Institute of Fundamental Research)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Questions about decomposition of representations of groups over local fields to subgroups, such as from SO(n) to SO(n-1), has been of considerable interest in the recent past with impressive works of Waldspurger, Moeglin-Waldspurger, and Raphael Beuzart-Plessis. Corresponding global question for unitary groups has been partly settled by Wei Zhang.
These questions have so far been considered only for tempered representations (of the group and the subgroup). In this lecture, I will discuss the situation with non-tempered representations. This is a report on work done with B. Gross and Wee Teck Gan.
- Supplements
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Dec 04, 2014
Thursday
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09:30 AM - 10:30 AM
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Modularity of non-semisimple Galois representations
Henri Darmon (McGill University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:00 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:00 AM - 12:00 PM
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The Bloch Kato Conjecture for some Adjoint Selmer Groups.
Frank Calegari (Northwestern University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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We prove some new vanishing results for the Bloch-Kato Selmer groups of Adjoint motives. This is joint work with David Geraghty.
- Supplements
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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02:00 PM - 03:00 PM
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Euler System
Sarah Zerbes (ETH Zürich)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
I show how Beilinson's Eisenstein symbol give rise to motivic cohomology classes attached to pairs of modular forms of weight >= 2. These motivic cohomology classes can be used to construct an Euler system -- a compatible family of global cohomology classes -- attached to pairs of modular forms, related to the critical values of the corresponding Rankin-Selberg L-function. This is joint work with Kings and Loeffler, extending my previous work with Lei and Loeffler for weight 2 forms. This Euler system has several arithmetic applications, including one divisibility in the Iwasawa main conjecture for modular forms over imaginary quadratic fields, and cases of the finiteness of Tate--Shafarevich groups for elliptic curves twisted by dihedral Artin representations.
- Supplements
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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03:30 PM - 04:30 PM
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p-adic L-functions, Iwasawa theory, and elliptic curves
Christopher Skinner (Princeton University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
This talk will describe some recent applications of p-adic L-functions and Iwasawa theory to the arithmetic of elliptic curves, especially to establishing the p-parts of the the Birch-Swinnerton-Dyer formula in cases of rank at most one.
- Supplements
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Dec 05, 2014
Friday
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09:00 AM - 10:00 AM
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G-bundles and the local Langlands correspondence
Laurent Fargues (Institut de Mathématiques de Jussieu)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Given a reductive group G over the p-adic numbers I will explain a classification result for G-bundles over the curve defined in my joint work with Fontaine. I will then state and explain a conjecture linked to this classification
- Supplements
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10:00 AM - 10:30 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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10:30 AM - 11:30 AM
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On conductor 1 algebraic automorphic representations of GL(n) over Q, and applications
Gaetan Chenevier (Centre National de la Recherche Scientifique (CNRS))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
In this talk, I will present some results concerning the classification of the cuspidal automorphic representations of GL(n) over Q whose archimedean component is `` algebraic ‘’ and whose non archimedean components are all unramified. As an application, I will sketch a proof of the following result : there are exactly 23 Siegel modular cusp forms of weight 12, for the full Siegel modular group, in genus at most 12.
- Supplements
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11:30 AM - 12:00 PM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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12:00 PM - 01:00 PM
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P-radicial base change,mod p
Laurent Clozel (Université de Paris XI)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
A new method introduced by Treumann, Venkatesh and the speaker makes it possible to prove cases of Langlands functoriality for cohomology classes mod p. I will show how this implies, in this context, automorphic induction for radicial extensions E=F(x^(1/p)) of number fields. I will also discuss the application to endoscopy for unitary groups.
- Supplements
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05:00 PM - 07:00 PM
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Bluegrass Performance
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Bluegrass performance in Simons Auditorium.
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