Séminaire de Géométrie Enumérative

Année 2019  2020 Temps : Vendredi à 10h30 Lieu : Jussieu, 1516  413 Institut de Mathématiques de Jussieu  Paris Rive Gauche, Sorbonne Université 
Date  Orateur  Titre et résumé  Lieu 
27/09/2019 
Yanqiao Ding,
IMJPRG et Zhengzhou University 
Genus decreasing phenomenon of higher genus Welschinger invariants Shustin introduced a invariant of del Pezzo surfaces to count real curves of positive genera. By considering the properties of these invariants under morse transformation, we found a genus decreasing phenomenon for these invariants. In this talk, we will present a genus decreasing formula for these invariants and discuss possible generalization of it. 
Jussieu, 1516  413 
18/10/2019 
Hülya Argüz, Université Versailles StQuentin 
Real Lagrangians in CalabiYau Threefolds We compute the mod 2 cohomology of the real Lagrangians in CalabiYau threefolds, using a long exact sequence linking it to the cohomology of the CalabiYau. We will describe this sequence explicitly, and as an application will illustrate this computation for the quintic threefold. This is joint work with Thomas Prince and with Bernd Siebert. 
Jussieu, 1516  413 
15/11/2019 
Xavier Blot, IMJPRG 
The quantum WittenKontsevich series The WittenKontsevich series is a generating series of intersection numbers on the moduli space of curves. In 2016, Buryak, Dubrovin, Guéré and Rossi defined an extension of this series using a quantization of the KdV hierarchy based on the geometry of double ramification cycle. This series, the quantum WittenKonstevich series, depends on a quantum parameter. When this quantum parameter vanishes, the quantum WittenKontsevich series restricts to the WittenKontsevich series. In this talk, we will first construct the quantum WittenKontsevich series and then present all the known results about its coefficients. Surprisingly, a part of these coefficients are expressed in terms of Hurwitz numbers. 
Jussieu, 1516  413 
21/11/2019 16h 
Yizhen Zhao, IMJPRG 
LandauGinzburg/CalabiYau correspondence for a complete intersection via matrix factorizations In this talk, I will introduce two enumerative theories coming from a variation of GIT stability condition. One of them is the GromovWitten theory of a CalabiYau complete intersection; the other one is a theory of a family of isolated singularities fibered over a projective line, which is developed by Fan, Jarvis, and Ruan recently. I will show these two theories are equivalent after analytic continuation. For CalabiYau complete intersections of two cubics, I will show that this equivalence is directly related  via Chern character  to the equivalences between the derived category of coherent sheaves and that of matrix factorizations of the singularities. This generalizes ChiodoIritaniRuan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces. 
Jussieu, 1525  502 
28/11/2019 15h15 
Grigory Mikhalkin, Université de Genève 
Separating semigroup of real curves and other questions from
a 1dimensional version of Hilbert's 16th problem Kummer and Shaw have introduced the separating semigroup Sep(S) of a real curve S. The semigroup is made of topological multidegrees of totally real algebraic maps from S to the Riemann sphere and can be considered in the context of a 1dimensional version of Hilbert's 16th problem. We'll explore this point of view and classify Sep(S) for curves of genera up to four. 
Jussieu, 1525  502 
05/12/2019 16h 
Danilo Lewanski, IPhT 
ELSVtype formulae The celebrated ELSV formula expresses Hurwitz numbers in terms of intersection theory of the moduli space of stable curves. Hurwitz numbers enumerate branched covers of the Riemann sphere with prescribed ramification profiles. Since the original ELSV was found, many more ELSVtype formulae appeared in the literature, especially in connection with EynardOrantin topological recursion theory. They connect different conditions on the ramification profiles of the Hurwitz problem with the integration of different cohomological classes which have been studied independently. We will go through this interplay, focusing on a conjecture proposed by Zvonkine and a conjecture of Goulden, Jackson, and Vakil. In both these conjectures, classes introduced by Chiodo play a key role. 
Jussieu, 1525  502 
16/01/2020 16h 
Sergey Finashin, Ankara, Middle East Technical University 
The first homology of real cubics are generated by real lines In a joint work with V. Kharlamov, we suggest a short proof of O. Benoist and O. Wittenberg theorem (arXiv:1907.10859) which states that for each real nonsingular cubic hypersurface X of dimension ≥2 the real lines on X generate the whole group H_1(X(ℝ);ℤ/2). 
Jussieu, 1525  502 
30/01/2020 16h 
Sybille Rosset, Université Versailles StQuentin 
A comparison formula in quantum Ktheory of flag varieties I will present here a correspondence between wellchosen quantum Ktheoretical GromovWitten invariants of different flag varieties. I will also discuss how this correspondence implies some finiteness properties of the big quantum Kring of flag varieties. 
Jussieu, 1525  502 
06/02/2020 15h30 
Conan Leung, The Chinese University of Hong Kong 
Geometry of MaurerCartan equation Motivated from Mirror Symmetry near large complex structure limit, a dgBV algebra will be constructed associated to a possibly degenerate CalabiYau variety equipped with local thickening data. Using this, we prove unobstructedness of smoothing of degenerated Log CY satisfying HodgedeRham degeneracy property. 
Jussieu, 1525  502 
27/02/2020 16h 
Karim Adiprasito, University of Copenhagen and Hebrew University of Jerusalem 
From toric varieties to embedding problems and l^2 vanishing conjectures I will survey a rather intruiging approach to some problems in geometric topology that start by reformulating them as problems in intersection theory. I will start by explaining, on a specific problem, biased pairing theory, which studies the way that the HodgeRiemann bilinear relation degenerates on an ideal, and review how this limits for instance the complexity of simplicial complex embeddable in a fixed manifold. I will then discuss a conjecture of Singer concerning the vanishing of l^2 cohomology on nonpositively curved manifolds, and use biased pairing theory to relate it to Hodge theory on a Hilbert space that arises as the limit of Chow rings of certain complex varieties. 
Jussieu, 1525  502 
13/03/2020 10h30 
Massimo Pippi, Institut de Mathématiques de Toulouse 
Séance reportée Réalisations motivique et ladique de la catégorie des singularités d'un modèle LG twisté Un modèle de LandauGinzburg twisté est un couple (X,s), où X est un schéma (sur une base S) et s est une sectionne globale d'un fibré en droites L sur X. Dans cet exposé, nous allons étudier la réalisation motivique (et ladique) de la catégorie de singularités attachées à un modèle de LandauGinzburg twisté. Pour faire ça, on devra introduire un formalisme de cycles évanescents approprié. Tous ça, ainsi qu'un théorème du a D.Orlov et à J.BurkeM.Walker, nous permettra de calculer la réalisation ladique de la catégorie des singularités de la fibre spécial d'un schéma régulier sur un anneau noetherien, local régulier de dimension n. Cette formule généralise un résultat du à A.BlancM.RobaloB.ToënG.Vezzosi, qui a fortement inspiré ce travail. 
Jussieu, 1516  413 