*(Programme en construction)*

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**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** - *titre à venir*

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**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*

**Sophie Marques** - *titre à venir*

**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)