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Séminaire de Géométrie Enumérative
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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,
IMJ-PRG 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 |
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18/10/2019 |
Hülya Argüz, Université Versailles St-Quentin |
Real Lagrangians in Calabi-Yau Threefolds We compute the mod 2 cohomology of the real Lagrangians in Calabi-Yau threefolds, using a long exact sequence linking it to the cohomology of the Calabi-Yau. 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 |
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15/11/2019 |
Xavier Blot, IMJ-PRG |
The quantum Witten-Kontsevich series The Witten-Kontsevich 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 Witten-Konstevich series, depends on a quantum parameter. When this quantum parameter vanishes, the quantum Witten-Kontsevich series restricts to the Witten-Kontsevich series. In this talk, we will first construct the quantum Witten-Kontsevich 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 |
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21/11/2019 16h |
Yizhen Zhao, IMJ-PRG |
Landau-Ginzburg/Calabi-Yau 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 Gromov-Witten theory of a Calabi-Yau 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 Calabi-Yau 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 Chiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces. |
Jussieu, 1525 - 502 |
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28/11/2019 15h15 |
Grigory Mikhalkin, Université de Genève |
Separating semigroup of real curves and other questions from
a 1-dimensional 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 1-dimensional 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 |
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05/12/2019 16h |
Danilo Lewanski, IPhT |
ELSV-type 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 ELSV-type formulae appeared in the literature, especially in connection with Eynard-Orantin 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 |
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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 non-singular cubic hypersurface X of dimension ≥2 the real lines on X generate the whole group H_1(X(ℝ);ℤ/2). |
Jussieu, 1525 - 502 |
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30/01/2020 16h |
Sybille Rosset, Université Versailles St-Quentin |
A comparison formula in quantum K-theory of flag varieties I will present here a correspondence between well-chosen quantum K-theoretical Gromov-Witten invariants of different flag varieties. I will also discuss how this correspondence implies some finiteness properties of the big quantum K-ring of flag varieties. |
Jussieu, 1525 - 502 |
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06/02/2020 15h30 |
Conan Leung, The Chinese University of Hong Kong |
Geometry of Maurer-Cartan equation Motivated from Mirror Symmetry near large complex structure limit, a dgBV algebra will be constructed associated to a possibly degenerate Calabi-Yau variety equipped with local thickening data. Using this, we prove unobstructedness of smoothing of degenerated Log CY satisfying Hodge-deRham degeneracy property. |
Jussieu, 1525 - 502 |
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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 Hodge-Riemann 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 non-positively 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 |
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13/03/2020 10h30 |
Massimo Pippi, Institut de Mathématiques de Toulouse |
Séance reportée Réalisations motivique et l-adique de la catégorie des singularités d'un modèle LG twisté Un modèle de Landau-Ginzburg 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 l-adique) de la catégorie de singularités attachées à un modèle de Landau-Ginzburg 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.Burke-M.Walker, nous permettra de calculer la réalisation l-adique 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.Blanc-M.Robalo-B.Toën-G.Vezzosi, qui a fortement inspiré ce travail. |
Jussieu, 1516 - 413 |