Activities 2009

Guests:

-Luca Moci (Roma) February 11, 2009.
-Nobuo Tsuzuki (Hiroshima)  February 15-21, 2009.
-Irene Bouw (Ulm) March 2-7, 2009. “Billiards and differential equations with integral solutions." March 4, 2009, 2AB/40, 16:15
-Stefan Wewers (Hannover) March 2-7, 2009.
-Lionel Fourquaux (Rennes), March, 5-11, 2009.
-Fumiharu Kato March 9-22. “Topological rings in rigid cohomology” March 11, 2009, 2AB/45, 16:30
-Fabien Trihan (Nottingham) Monday, March 30, 2009 15:30, 2AB/40: "On the geometric analogue of Iwasawa's main conjecture for abelian varieties".
-Pierre Berthelot (Rennes) March 27-April?
"Rational points over finite fields for regular models of algebraic varieties of Hodge level >=1", March 30, 2009, 14:15, 2AB40
-Ted Chinburg (Philadelphia), March 30- April 2. "Actions of finite groups on power series rings" March 31, 2009, 1A/150, 16:00
-Michele Bolognesi "The Stack of Trigonal Curves and its Picard Group" April, 6, 2009, 2BC/30 15:30
-Gianluca Pacienza (Strasburgo) April 20, 2009 "Sulla geometria dei luoghi base stabili di divisori aggiunti e anti-aggiunti" 2BC/30, 14:00
-Vincent Maillot (Jussieu) April 24, 2009 “Units, automorphic forms and arithmetic Riemann-Roch” 1AC/30, 11:30
-F. Pop (Pennsylvania) April 30, 2009, 1AD50 16:30 "On the birational p-adic section conjecture"

-Y. André (ENS) “Slope filtrations I” Outline of a general theory May 14, 2009, 16:30 2BC/60, “Slope filtrations II” May 21, 2009, 16:30 2BC/60
-A. Rigato (Roma 2) May 25, 2009 “Uniqueness of low genus optimal curves over F2 ”14:30, 2BC/30
-E. Urban (Columbia Un. NY) June 4, 2009 Provisional title “Elliptic curves, modular forms and Hida families” June 4, 2009, 9:30 1AD/30
-Katherine Stevenson,California State University, Northridge, January-July, 2009
“Solving embedding problems for subgroups of the fundamental group of a curve”May 28th, 2009, in room 1AD/30, h.9:30
-K. Loerke (Muenster) July 5-18, 2009
-Boas Erez (Bordeaux) September 20-26. “Ramificazione e azioni moderate di gruppi”, September 24, 14:30, room 2AB40
-Y. André September 22-29., 2009
-Amnon Besser September 27-October 1, 2009
“The syntomic regulator for K_1 of surfaces” September 29, 16:00 room 2BC60
Abstract:
We consider certain elements in the algebraic K-group K_1 of a surface, given by a collection of curves on the surface together with rational functions on these curves such that the sum of all their divisors on the surface vanishes. These elements have been widely studied in algebraic and arithmetic geometry. For surfaces over the complex numbers their Beilinson regulators have been computed by Beilinson. We provide an analogous formula for surfaces over p-adic fields (under certain integrality assumptions) for the regulator into syntomic cohomology.
- Nicola Mazzari, October 2 & 9, 2009, Vanishing cycles.
-Dajano Tossici (Pisa) October 12-14, 2009. “Geometric classification of models of \mu_{p2,K}” October 13, 2BC60, 9:30
Abstract: Let R be a discrete valuation ring  and let K be its fraction field. In this talk, after recalling the well known
 classification of models of \mu_{p,K}, we will give an idea of the classification of models of \mu_{p2,K}, i.e. finite and flat group schemes over R which are isomorphic to  \mu_{p2,K} over K. The main features of our classification are the following: 1) the parameters can be easily
interpretated geometrically; 2) the description of the models is explicit 3)  any model can be seen as the kernel of an exact sequence which coincides generically with the Kummer sequence. This sequence let us to generalize the Kummer Theory in order to describe torsors under these group schemes. The main tool which we use is the  Sekiguchi-Suwa Theory, which we will briefly recall. If we will have enough time we will compare our work with the recent works of Breuil and Kisin about the  classification of finite and flat goup schemes over  d.v.r (with some hypothesis) killed by p^n.
-Yves Laurent (Grenoble), October 16, 2009, “D-modules and Lie groups: a proof of Kirillov's conjecture''.
Abstract: In the theory of Lie groups, the irreducibility of a unitary representation is not preserved in general by restriction to a
subgroup. Kirillov's conjecture says that it is preserved for the groups Sl(n,R) or Sl(n,C) when the subgroup is a maximal parabolic subgroup.
This conjecture was proved by Barush using a detailed study of nilpotent orbits. In fact, it is not difficult to see that the conjecture is equivalent
to the fact that some system of partial differential equations has no singular distributions as solutions. This system of equations is a regular
holonomic D-module and we give a proof of the result by an explicit calculation of the roots of the b-functions associated to this D-module.
-P. Polesello “Varietà di Jacobi complesse e quantizzazione” October 23, 2009, 2AB40, 14:30
Abstract: Le varieta' di Jacobi, introdotte indipendentemente da Kirillov e Lichnerowicz, sono sostanzialmente dei quozienti di varieta' di Poisson omogenee. In questo seminario richiamero' la definizione di varieta' di Jacobi complessa, dandone vari esempi, e spieghero' cosa vuol dire "quantizzare" una tale varietà. Il problema dell'esistenza e della classificazione delle quantizzazioni si risolve usando le tecniche della "formalità" di Kontsevich. In particolare si ottiene che per le varieta' di contatto la classificazione e' governata da un certo complesso di de Rham logaritmico
-B. Chiarellotto. “Log-structures, vanishing cycles and limit Hodge structures” October 20, 2009, 2AB45, 9:45, October 30, 2AB45, 9:30, November 3&10 &17, 2AB45, 9:45

Abstract: We will justify the idea of limit hodge structure both from the topological/analytic
point of view  (Steenbrink) and in the etale case with coefficients over  ${\bf Q}_l$, $l\not= p$  (Deligne and Serre: zeta functions for varieties over a number field and the their local zeta factors at bad primes).
We will show how to construct such a Mixed Hodge Structure on the generic fiber  via vanishing cycles and log-de Rham Complexes.
We will justify then the use of $log$-crystalline cohomology for the semistable case as "vanishing-cohomology or limit MHS".
-G. Morando “Some aspects of the Riemann-Hilbert correspondence on complex curves” November 6, 2009. 2AB40, 14:30

-Florian Ivorra (Rennes) December 7-12, 2009, talk “Motives over a general base” December 11, 2AB40 9:45
-Marco Boggi (Universidad de los Andes - Bogota' (Colombia) December, 15, “Sulla fedeltà delle rappresentazioni di Galois associate a curve iperboliche” 2AB40 11:30

-Johannes Nicaise (Lille) December 14-22, 2009, December, 18, “A proof of the motivic monodromy conjecture for abelian varieties” 1BC50 9:45
-A. Bertapelle “Vanishing cycles and Steenbrink's spectral sequence over a dvr” November 24, 2009, December 1, 2AB45, 9:45, January 18, 2010, 2AB40, 15:30