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DTSTART;TZID=Europe/Paris:20241105T133000
DTEND;TZID=Europe/Paris:20241105T143000
DTSTAMP:20260408T094707
CREATED:20240830T140936Z
LAST-MODIFIED:20241108T090125Z
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SUMMARY:AG : Sabyasachi Dhar (Indian Institute of Technology) : Tate cohomology and local base change of generic representations of \( \mathrm{GL}_n \)
DESCRIPTION:Cet exposé est en distanciel.\n  \nAbstract: Let \( K \) be a number field and let \( G \) be a connected reductive algebraic group defined over \( K \). Let \( \sigma \) be an automorphism of \( G \) of prime order \( l \). In the foundational work [TV16]\, Treumann and Venkatesh established a functoriality lifting of mod-\( l \) Hecke eigenvalues of \( G^{\sigma} \) to mod-\( l \) Hecke eigenvalues of \( G \)\, where \( G^{\sigma} \) is the connected component of the fixed points of \( \sigma \). They also made some conjectures for representation theory of \( p \)-adic groups and these conjectures predict that the (local) functoriality lifting is compatible with Tate cohomology for the action of \( \langle \sigma \rangle \).\n\nIn this talk\, we discuss this conjecture in the setting of cyclic base change for the general linear group \( G = \mathrm{GL}_n \). Say \( F \) is a finite extension of \( \mathbb{Q}_p \) and let \( E \) be a finite Galois extension of \( F \) with degree of extension \( l \)\, where \( l \) and \( p \) are distinct primes. Let \( \pi \) be an irreducible integral \( l \)-adic representation of \( \mathrm{GL}_n(F) \)\, and \( \Pi \) be an irreducible integral \( l \)-adic representation of \( \mathrm{GL}_n(E) \) obtained as base change lift of \( \pi \). Then there are two representations of \( \mathrm{GL}_n(F) \)\, defined over \( \overline{\mathbb{F}}_l \)\, namely the mod-\( l \) reduction \( r_l(\pi) \) and the Tate cohomology group \( \widehat{H}^i(\sigma\, \Pi) \)\, \( i \in \{0\, 1\} \)\, for the action of \( \langle \sigma \rangle \) on \( \Pi \). Treumann–Venkatesh’s conjecture relates these two representations. We discuss this in the case where \( \pi \) and \( \Pi \) are both generic\, and \( l \) does not divide the order of \( \mathrm{GL}_{n-1}(\mathbb{F}_q) \) for \( n \geq 3 \)\, where \( q \) is the cardinality of the residue field of \( F \).\n  \n[TV16] David Treumann and Akshay Venkatesh\, Functoriality\, Smith theory\, and the Brauer homomorphism\, Ann. of Math. (2) 183 (2016)\, no. 1\, 177–228. MR 3432583
URL:https://lmv.math.cnrs.fr/evenenement/ag-sabyasachi-dhar-indian-institute-of-technology/
CATEGORIES:Séminaire AG
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20241112T080000
DTEND;TZID=Europe/Paris:20241112T170000
DTSTAMP:20260408T094707
CREATED:20240826T100821Z
LAST-MODIFIED:20241118T133304Z
UID:12959-1731398400-1731430800@lmv.math.cnrs.fr
SUMMARY:AG : Journée du séminaire différentiel
DESCRIPTION:Il n’y aura pas d’exposé au séminaire AG.  Voir ici pour les informations sur le séminaire différentiel. \n\n10:30-11:30: Florian Fürnsinn\, Fuchs’ Theorem\, an Exponential Function\, and Abel’s Problem in Positive Characteristic\nAbstract: In the 19th century Fuchs and Frobenius developed a local solution theory for regular singular ordinary linear differential equations with complex polynomial coefficients. The Grothendieck -curvature conjecture motivates the search for a similar theory for equations whose coefficients are polynomials over fields of positive characteristic. In this talk I will define a differential extension of the power series over a field of positive characteristic \, making use of new variables behaving under differentiation like iterated logarithms in characteristic zero. Every regular singular ordinary linear differential equation with polynomial or power series coefficients over admits a full basis of solutions in this extension. In particular\, the exponential differential equation has a solution . Such solutions have remarkable properties\, which we will explore. For example\, I will discuss an analogue of Abel’s problem about the algebraicity of logarithmic integrals over. This talk is based on joint work with H. Hauser and H. Kawanoue.\n\n  \n\n12:00-14:00: repas.\n\n  \n\n14:15-15:15: Claudia Fevola\, Euler discriminant of hyperplane arrangements\nAbstract: The Euler discriminant describes the locus of coefficients that cause a drop in the Euler characteristic of a very affine variety. In this talk\, we focus on the case where the variety is the complement of hyperplanes. I will present formulas for two specific scenarios: when the coefficients are sparse and when they are restricted to a subspace of the parameter space. These formulas enable the computation of singularities in Euler integrals of linear forms\, with applications in cosmology. This is joint work with Saiei Matsubara-Heo. \n\n\n  \n\n15:30-16:30: Antoine Chambert-Loir\, Rationality and potential\nAbstract: A 1894 theorem by Émile Borel asserts that a power series with integral coefficients that defines a meromorphic function on a disk of radius > 1 is the Taylor expansion of a rational function. It has been extended in various directions (Pólya\, Dwork\, Bertrandias and Robinson) to encompass more complicated shapes than open disks\, number fields\, and several absolute values. We extend to algebraic curves of arbitrary genus the theorem of Cantor that considers Taylor expansions “at several points”. Our proof runs in two steps. The first step is an algebraicity criterion\, which is proved using a method of diophantine approximation. The second step relies on the Hodge index theorem in Arakelov geometry\, following an earlier work by Bost and myself. (Joint work with Camille Noûs) “Potentiel et rationalité”\, arXiv:2305.17210
URL:https://lmv.math.cnrs.fr/evenenement/ag-journee-du-seminaire-differentiel/
CATEGORIES:Séminaire AG,Séminaire différentiel
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20241119T133000
DTEND;TZID=Europe/Paris:20241119T143000
DTSTAMP:20260408T094707
CREATED:20240902T111255Z
LAST-MODIFIED:20241122T160955Z
UID:13073-1732023000-1732026600@lmv.math.cnrs.fr
SUMMARY:AG : Merlin Christ (IMJ-PRG) : Cluster categories and Fukaya categories of surfaces
DESCRIPTION:The talk is split into two parts (each 45 mins with a 30min break) \nPart 1: Introduction to cluster algebras and cluster categories of surfaces \nCluster algebras of surfaces are fundamental examples in the theory of cluster algebras. They can be understood very explicitly in terms of combinatorial geometry of surfaces. After an introduction to these\, we will gently explain what a categorification of a cluster algebra in terms of a triangulated category (the so-called cluster  category) is. \nPart 2: Topological Fukaya categories and the Higgs category \nWe first recall the construction of the topological Fukaya category of a surface in terms of a constructible cosheaf of dg-categories. We then present a description of the relative version of the cluster category of a marked surface (called the Higgs category) in terms of a topological Fukaya category valued in a 1-CY cosingularity category.
URL:https://lmv.math.cnrs.fr/evenenement/ag-merlin-christ-imj-prg/
CATEGORIES:Séminaire AG
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20241126T133000
DTEND;TZID=Europe/Paris:20241126T143000
DTSTAMP:20260408T094707
CREATED:20240904T130452Z
LAST-MODIFIED:20241129T130312Z
UID:13082-1732627800-1732631400@lmv.math.cnrs.fr
SUMMARY:AG : Olivier Piltant (LMV / CNRS) : Approche Hironakienne du problème de Résolution des Singularités en caractéristique positive
DESCRIPTION:La Conjecture de résolution de Grothendieck prédit qu’un schéma excellent réduit est l’image d’un schéma régulier par un morphisme propre et birationnel. Elle a été établie en caractéristique résiduelle nulle (Hironaka\, Bennett\, Bierstone-Milman\, Villamayor) mais reste encore largement ouverte lorsque celle-ci est positive. \nDans un premier temps\, je présenterai l’idée générale de la stratégie de Hironaka (stratification par des invariants semicontinus\, éclatements permis et récurrence sur la dimension) ainsi que les difficultés spécifiques à la caractéristique positive. \nDans un deuxième temps\, j’expliquerai comment ces difficultés ont pu être résolues en dimension trois\, en collaboration avec V. Cossart (2019)\, et pourquoi la stratification du lieu singulier des sous-groupes additifs de l’espace affine sur un corps non parfait joue un rôle majeur en dimension supérieure (collaboration avec V. Cossart et B. Schober).
URL:https://lmv.math.cnrs.fr/evenenement/ag-olivier-piltant-lmv-cnrs/
CATEGORIES:Séminaire AG
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