Séminaire de Géométrie Enumérative


Contacts :
Penka Georgieva
Ilia Itenberg


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
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
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
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
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
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
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
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
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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