Talks

(Programme under construction)

Federico Bambozzi - Tempered cohomology of varieties in characteristic p

Abstract: In this talk I explain how to use methods of derived geometry to define the notion of tempered tube of a variety in characteristic p. Such tubes naturally appear in the theory of p-adic differential equations. This permits to define a tempered version of p-adic cohomology for smooth varieties. This work is in collaboration with Bruno Chiarellotto and Pietro Vanni.

Anna Cadoret - Introduction aux faisceaux pervers

Résumé. On présentera brièvement la notion de coeur d'une catégorie dérivée et la construction de la catégorie des faisceaux pervers dans la situation de recollement. On tentera également de donner quelques motivations pour l'introduction des catégories de faisceaux pervers. 

Cyrille Chenavier - Computation of Koszul homology and application to partial differential systems

 Abstract: The formal integrability of systems of partial differential equations plays a fundamental role in different analysis and synthesis problems for both linear and nonlinear differential control systems. Following Spencer's theory, to test the formal integrability of a system of partial differential equations, we must study when the symbol of the system, namely, the top-order part of the linearization of the system, is 2-acyclic or involutive, i.e., when certain Spencer cohomology groups vanish. Using the well-known fact that Spencer cohomology is dual to Koszul homology and symbolic computation methods, we show how to effectively compute the homology modules defined by the so-called Koszul complex of a finitely presented module over a commutative polynomial ring. These results are implemented using the OreMorphisms package. We then use these results to effectively characterize 2-acyclicity and involutivity of the symbol of a system of partial differential equations. Finally, we show explicit computations on different examples.

Qing Liu - Regular models of hyperelliptic curves over discrete valuation rings

Abstract: In this talk I will explain how to apply Lipman's method to resolve the singularities of double covers of regular surfaces. This leads in particular to an algorithm to finding a regular model over the ring of integers for hyperelliptic curves defined over the rational numbers. Such a regular model contains quite a few interesting information concerning the arithmetical  properties of the curves. It can also help to decide whether two hyperelliptic curves over the rationals are isomorphic.

Frank Neumann - Actions of Frobenii for moduli stacks of principal bundles

Abstract: We study the various arithmetic and geometric Frobenius morphisms on the moduli stack of principal bundles over a smooth projective algebraic curve and determine explicitly their actions on the l-adic cohomology of the moduli stack in terms of Chern classes. Joint work with A. Castorena (CCM-UNAM)