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DTSTART;TZID=Europe/Paris:20260521T133000
DTEND;TZID=Europe/Paris:20260521T170000
DTSTAMP:20260521T120550
CREATED:20260518T131737Z
LAST-MODIFIED:20260518T142112Z
UID:15040-1779370200-1779382800@lmv.math.cnrs.fr
SUMMARY:Soutenance de thèse : Danil Gubarevich : On Gromov-Witten invariants and the Hall induction
DESCRIPTION:Danil Gubarevich soutient sa thèse\,  intitulée « On Gromov-Witten invariants and the Hall induction » encadrée par Dimitri Zvonkine\, le jeudi 21 mai\, 13h30\, bâtiment Fermat\, salle 2201. \n  \nRésumé : \nThe first two chapters of the manuscript provide the motivation for the subjects we were studying in this thesis. First we discuss the relation between the Gromov-Witten and Donaldson-Thomas enumerative theories and explain how the DT-theory was categorified by means of perverse sheaves of vanishing cycles. This part aims to show the link between Chapters 3 and 4. \nFurther we review the generalities on genus 0 Gromov-Witten theory with the focus on smooth complete intersections\, relevant to Chapter 3. \nTo motivate Chapter 4\, we review the notions of the classical Hall algebra of a finitary hereditary category and its cohomological enhancement by the cohomological Hall algebra\, using quiver representations as a key example. These algebras serve as the primary inspiration for the constructions and theorems discussed in Chapter 4. \nFinally\, we state the results of our thesis. \nChapter 3 discusses GW-theory of even dimensional complete intersections X of two quadrics in CP^{m+2}. These varieties are exceptional from the point of view of the Gromov-Witten theory: they are (together with surfaces of degrees 2 and 3) the only complete intersections whose Gromov-Witten theory is not invariant under the full orthogonal or symplectic group acting on the primitive cohomology. The genus 0 Gromov-Witten theory of X was studied by Xiaowen Hu. He used geometric arguments and the associativity of quantum cohomology to compute all genus 0 correlators except one\, which cannot be determined by his methods. In our paper\, we use a different method\, based on Jun Li’s degeneration formula. We show [Theorem (??)] the existence of a basis in cohomology of X\, such that the remaining Gromov-Witten invariant in this basis vanishes. \nIn Chapter 4 we study an example of the Hall induction\, the natural analog of the Hall multiplication in situations where the moduli space at hand is not the moduli space of objects in some abelian category. We study the Hall induction for the moduli space T^*(V/G): the cotangent stack of the quotient stack V/G\, where V is a representation of a complex reductive group G. First we indicate how to define the Hall induction map via a representation of a Levi subgroup on the level of the critical Hall induction and then conjugate this map by the dimensional reduction isomorphism. We adapt a result proven for cohomological and K-theoretical Hall algebras of a quiver: the first is the torsion freeness of the Hall induction for the stack T^*(V/G) deformed by a certain torus T_s. This result is equivalent to an embedding of the Hall induction into the space of symmetric polynomials. As a corollary\, we prove that the T_s-equivariant Borel-Moore homology of T^*(V/G) is concentrated in even homological degrees.
URL:https://lmv.math.cnrs.fr/evenenement/soutenance-de-these-danil-gubarevich-on-gromov-witten-invariants-and-the-hall-induction/
CATEGORIES:Soutenance de thèse
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DTSTART;TZID=Europe/Paris:20260521T140000
DTEND;TZID=Europe/Paris:20260521T150000
DTSTAMP:20260521T120550
CREATED:20260308T171641Z
LAST-MODIFIED:20260511T133220Z
UID:14846-1779372000-1779375600@lmv.math.cnrs.fr
SUMMARY:EDP : Daniel Han-Kwan (université de Nantes et CNRS) : Limite semiclassique de NLS cubique pour les états mixtes
DESCRIPTION:Résumé :\nOn considère la limite semiclassique de l’équation de Schrödinger cubique pour les états mixtes. La limite formelle est une équation de Vlasov singulière (Vlasov-Benney dans le cas défocalisant).\nCette limite est justifiée pour des données initiales à régularité finie\, vérifiant une condition de stabilité de type Penrose. \nIl s’agit d’une collaboration avec Frédéric Rousset (Orsay).
URL:https://lmv.math.cnrs.fr/evenenement/edp-daniel-han-kwan-universite-de-nantes-et-cnrs/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260521T153000
DTEND;TZID=Europe/Paris:20260521T163000
DTSTAMP:20260521T120550
CREATED:20260308T171802Z
LAST-MODIFIED:20260511T114105Z
UID:14848-1779377400-1779381000@lmv.math.cnrs.fr
SUMMARY:EDP : Philippe Souplet (université Sorbonne Paris Nord) : Classification of entire and ancient solutions of the diffusive Hamilton-Jacobi equation
DESCRIPTION:Abstract: (joint work with Loth Chabi) We study the Liouville type classification and symmetry properties\,\nin \(R^n\) and in a half-space with Dirichlet boundary conditions\, for entire and ancient solutions of the diffusive Hamilton-Jacobi equation\,\nwhich arises in optimal stochastic control\, in KPZ type models of surface growth and in studies of boundary gradient blow-up. \nIn particular we obtain optimal Liouville type theorems for ancient and entire solutions in \(R^n\) and we completely classify entire solutions in a half-space.\nThe proofs rely\, among other things\, on new and optimal\, local estimates of Bernstein and Li-Yau type.\nSuch Liouville type results are very useful in the qualitative analysis of blow-up singularities for this equation.
URL:https://lmv.math.cnrs.fr/evenenement/edp-philippe-souplet-universite-sorbonne-paris-nord/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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