Beat Zurbuchen (ETHZ)
Spreading out perverse sheaves and Kashiwara's conjectures abstract
Abstract:
<p>Kashiwara's conjectures are deep statements about the cohomology of semisimple perverse sheaves, including the decomposition theorem and the Hard Lefschetz theorem. I will describe a new specialization method for perverse sheaves, which allows one to extend geometrically irreducible perverse sheaves from the generic fiber to a relatively perverse sheaf over an arbitrary quasi-excellent base scheme. This specialization method implies Kashiwara's conjectures for arithmetic complexes and implies stronger semisimplicity statements than were available before. The goal of this talk is to describe the extension theorem and its applications. This is work in progress.</p>
13:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Pierre-Henri Cocquet
Schémas numériques avec correction de dispersion pour des problèmes de propagation d\'ondes abstract
Abstract:
L\'approximation numérique de problèmes de propagation d\'onde souffre de l\'erreur de dispersion.Cette dernière provient d\'une différence entre les vitesses de phase associées aux ondes des problèmes continu etdiscret. Elle implique de considérer des maillages très fins pour pouvoir être correctement prise en compte et ainsiobtenir des solutions numériques avec une précision fine.Dans ce séminaire, on commencera par présenter une technique de correction de dispersion pour l\'équation de Helmholtzdiscrétisée par différences finies. Cette méthode est basée sur l\'introduction d\'une perturbation du nombre d\'onde dansle schéma et permet notamment de réduire l\'erreur relative pour des maillages suffisamment fins.On montrera ensuite comment cette technique peut être étendue pour l\'équation des ondes temporelle.Enfin, on illustrera les effets de chaque méthode de correction proposée au travers d\'expériences numériques.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Ignacio Muñoz Jiménez (University of Genova)
Gross points in ordinary families of Hilbert modular forms abstract
Abstract:
he Gross--Zagier formula provides a fundamental link between central derivatives of L-functions and Heegner points on indefinite Shimura curves. In this talk, I will focus on the other side of the picture: the arithmetic of definite quaternion algebras and definite Shimura varieties. In this setting, I will explain how Gross points, the counterpart of Heegner points, can be used to construct an anticyclotomic p-adic L-function. I will then discuss how this construction interpolates in Hida families of modular forms, and I will conclude with a review of recent work extending these ideas to the totally real setting.
Prof. Dr. Patricia Alonso Ruiz (Friedrich Schiller University Jena)
Trying to solve cubic NLS on a fractal? Maybe not by fixed point if you start below Sobolev... abstract
Abstract:
Duhamel and the fixed point theorem are often your best allies when solving non-linear PDEs like the cubic non-linear Schrödinger equation (NLS). This PDE has its origins in quantum mechanics, and it plays a prominent role in the modeling of dispersive wave phenomena, as for instance Bose-Einstein condensation.Dispersion is affected by the nature of the underlying geometry of the space it evolves, and in this talk we will address the basic question: Can one solve the cubic NLS modeling dispersion on the Sierpinski gasket? The latter is a common prototype of a compact fractal set.To approach the problem, we will call our allies Duhamel and the fixed point theorem. With a mixture of surprise (?) and perplexity (?) we will realize they are of no help to prove existence of solutions when the initial data has regularity below the threshold for the Sobolev embedding. What a different picture than in the torus or the sphere! Afterwards, if time permits, we will connect this result to (the absence of) Strichartz estimates. In any case, excitement will fill the stage :)Results are part of joint work with Gigliola Staffilani (MIT).
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Hendrik Lenstra (Leiden University)
Polynomial-time algorithms in algebraic number theory abstract
Abstract:
This lecture requires no previous knowledge of algebraic number theory, as even the most elementary notions of that theory are computationally too complicated to be accessible by algorithms that run in polynomial time. Thus, the field described by the title is quite restricted in scope. The best results were obtained by means of a relatively recently developed technique that is closely related to the method of "blowing up" known from algebraic geometry. It is hoped that the latter field will also profit from the insights gained by the new algorithmic approach.The lecture represents joint work with Daan van Gent and Alexander Spieksma.
16:30 • UZH Zentrum, Building KO2, Room F 150