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Speakers Schedule Titles of talks Abstracts
Speakers
| P. Colmez | J. Heinloth | B. C. Ngô |
| J.-F. Dat | G. Henniart | G. Pappas |
| G. Faltings | M. Kisin | M. Reineke |
| L. Fargues | R. Kottwitz | E. Viehmann |
| T. Haines | S. Kudla | J.-L. Waldspurger |
| M. Harris | L. Lafforgue | T. Yoshida |
| U. Hartl | G. Laumon | Th. Zink |
Schedule
| Sun, Oct 5 | Mon, Oct. 6 | Tue, Oct. 7 | Wed, Oct 8 | Thu, Oct 9 | Fri, Oct 10 | |
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8:00-9:00
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Registration
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Registration
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9:00-10:00
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Colmez
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Hartl
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Ngô
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Dat
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Henniart
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10:00-10:30
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Coffee
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Coffee
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Coffee
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Coffee
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Coffee
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10:30-11:30
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Waldspurger
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Kottwitz
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Reineke
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Lafforgue
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Fargues
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11:45-12:45
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Viehmann
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Pappas
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Kudla
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Haines
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Laumon
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14:30 - 15:30
Registration
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14:30- Boat trip |
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15:00-15:30
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Coffee
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Registration/Coffee
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Coffee
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15:30-16:30
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Heinloth
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Faltings
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Yoshida
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15:10 - Excursion to Cologne |
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16:45-17:45
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17:00 - 20:00 Registration Wegelerstr. 10 |
Zink
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Harris
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Kisin
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17:45-18:15
Registration
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| 19:00 h- Banquet |
Titles of the talks
06.10.
| 9:00 | Pierre Colmez | On the p-adic local Langlands correspondence for GL2(Qp) |
| 10:30 | Jean-Loup Waldspurger | An integral formula related to the local Gross-Prasad conjecture |
| 11:45 | Eva Viehmann | Generalized affine Springer fibres associated to non-equivalued root valuation strata |
| 15:30 | Jochen Heinloth | On moduli spaces of G-bundles and their cohomology |
| 16:45 | Thomas Zink | A de Rham-Witt complex for rigid cohomology |
07.10.
| 9:00 | Urs Hartl | The Newton stratification on deformations of local shtuka |
| 10:30 | Guy Henniart | Clifford Theory for reductive p-adic groups |
| 11:45 | George Pappas | Phi-modules and coefficient spaces for Galois representations |
| 15:30 | Gerd Faltings | The isomorphism between Drinfeld's and Lubin-Tate's tower |
| 16:45 | Michael Harris | Functoriality and construction of automorphic Galois representations |
08.10.
| 9:00 | Bao Châu Ngô | The support of simple perverse sheaves in the decomposition theorem |
| 10:30 | Markus Reineke | Moduli spaces of representations of quivers |
| 11:45 | Stephen Kudla | Arithmetic cycles for unitary groups |
09.10.
| 9:00 | Jean-François Dat | Looking for a geometric interpretation of the (mod l) local Langlands correspondence |
| 10:30 | Laurent Lafforgue | Trying to build a kernel for functoriality: the case of unramified automorphic induction from GL(1) to GL(2) |
| 11:45 | Thomas Haines | Shimura varieties with Gamma_1(p)-level structure and Hecke algebra isomorphisms |
| 15:30 | Teruyoshi Yoshida | Remarks on Lubin-Tate theory |
| 16:45 | Mark Kisin | Shimura varieties mod p |
10.10.
| 9:00 | Robert Kottwitz | Dimensions and non-emptiness of affine Deligne-Lusztig varieties |
| 10:30 | Laurent Fargues | The p-adic geometry of moduli spaces of abelian varieties and p-divisible groups |
| 11:45 | Gérard Laumon | The weighted fundamental lemma |
Abstracts
Jean-François Dat: Looking for a geometric interpretation of the (mod l) local Langlands correspondence
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 prospect a geometric-cohomological interpretation of (some special cases) of the correspondence, using Drinfeld's spaces and their similarities with Deligne-Lusztig varieties.
Gerd Faltings: The isomorphism between Drinfeld's and Lubin-Tate's tower
The isomorphism between the two towers extends to other coverings of period domains. We explain the construction of such an isomorphism.
Laurent Fargues: The p-adic geometry of moduli spaces of abelian varieties and p-divisible groups
We first define and study an Hecke equivariant cellular parametrization by Bruhat-Tits buildings of the p-adic Berkovich spaces associated to the Lubin-Tate tower. We extend this to a parametrization by compactifications of those buildings of the whole unitary type with signature (1,n-1) Shimura varieties. We will then present a Harder-Narasimhan type theory that allows us to give such parametrizations for all Shimura varieties and moduli spaces of p-divisible groups.
Thomas Haines: Shimura varieties with Gamma_1(p)-level structure and Hecke algebra isomorphisms
This talk will discuss a program to study the reduction modulo p of Shimura varieties with Gamma_1(p)-level structure by relating them to Shimura varieties with Iwahori level structure. One ingredient is a base change fundamental lemma for central elements in the Hecke algebra associated to a type of the form (I,chi) (here chi is a character on an Iwahori subgroup I which is trivial on the pro-unipotent radical of I). This is joint work in progress with Michael Rapoport.
Urs Hartl: The Newton stratification on deformations of local shtuka
(joint work with Eva Viehmann) Bounded local shtuka are function field analogs for p-divisible groups. We describe their deformations and moduli spaces. The latter are analogous to Rapoport-Zink spaces for p-divisible groups. The underlying schemes of these moduli spaces are affine Deligne-Lusztig varieties. For basic Newton polygons the closed Newton stratum in the universal deformation of a local shtuka is isomorphic to the completion at the corresponding point of the affine Deligne-Lusztig variety. This yields bounds on the dimension and proves equidimensionality of the basic affine Deligne-Lusztig varieties.
Jochen Heinloth: On moduli spaces of G-bundles and their cohomology
This is a report on work on the geometry of moduli spaces of torsors under non-constant group schemes on curves. The basic geometric invariants of these spaces have been conjectured by Pappas and Rapoport. I’d like to explain how the more general setup helps to shorten the computation of these invariants and indicate that these results also suggest what the structure of the cohomology of these spaces should be.
Guy Henniart: Clifford Theory for reductive p-adic groups
(Joint work in progress with C. J. Bushnell): Let F be a p-adic field. The absolute Galois group G_F of F has a distinguished pro-p subgroup, the wild ramification subgroup P_F. Clifford Theory relates the irreducible representations of G_F to those of P_F. Via the Langlands correspondence, this can be conjecturally transferred, for a reductive group H over F, to a relation between irreducible smooth representations of G, and simple characters in the sense of Bushnell-Kutzko. We shall state results for H=GL(N,F), and speculations for classical groups over F.
Mark Kisin: Shimura varieties mod p
I will report on some recent progress on a conjecture of Langlands-Rapoport, describing the mod p points of a Shimura variety.
Robert Kottwitz: Dimensions and non-emptiness of affine Deligne-Lusztig varieties
The talk will report on joint work of Goertz-Haines-Kottwitz-Reuman on dimensions and non-emptiness of affine Deligne-Lusztig varieties in the affine flag manifold and will also review some of the other facts known about affine Deligne-Lusztig varieties.
Stephen Kudla: Arithmetic cycles for unitary groups
In this talk I will discuss recent joint work with Rapoport on arithmetic cycles for Shimura varieties associated to U(n-1,1). In particular, we establish a relation between the arithmetic degree of certain 0-cycles and the non-singular, non-degenerate, Fourier coefficients of the derivatives of certain incoherent Eisenstein series on U(n,n).
Eva Viehmann: Generalized affine Springer fibres associated to non-equivalued root valuation strata
(joint work with R. Kottwitz) For a given (possibly non-equivalued) root valuation datum we define and study a new kind of associated generalized affine Springer fibres. They are nonempty exactly over the closure of the given root valuation stratum and define interesting coverings of the given stratum.
Jean-Loup Waldspurger: An integral formula related to the local Gross-Prasad conjecture
Teruyoshi Yoshida: Remarks on Lubin-Tate theory
We treat a rather simple proof of local class field theory using Lubin-Tate theory, by showing the base change property directly from the Lubin-Tate construction.
Thomas Zink: A de Rham-Witt complex for rigid cohomology
Let $X$ be a smooth scheme over a perfect field $k$ of characteristic $p > 0$. We define a subcomplex of the de Rham-Witt complex of $X/k$ by a certain convergence condition. The hypercohomology of this subcomplex of Zariski sheaves on $X$ tensored with $\mathbb{Q}$ is the rigid cohomology of $X$. This is joint work with Andreas Langer and Christopher Davis.
