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symplectic [2024/12/02 11:30] – g.msymplectic [2025/05/04 18:57] (Version actuelle) – g.m
Ligne 1: Ligne 1:
 ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar ===== ===== GeNeSys: Geneva-Neuchâtel Symplectic geometry seminar =====
  
-**2024, December 6, day, Université de Genève**+Ìý
 +**2025, May 6, Tuesday, Université de Neuchâtel**Ìý
 +Ìý
 +  Marco Golla (Université de Nantes, CNRS) Ìý
 +  13h00, Salle B217Ìý
 +  Alexander polynomials and symplectic curves in CP^2Ìý
 +  Ìý
 +Libgober defined the Alexander polynomial of a (complex) plane projective curve and showed that it detects some Zariski pairs ofcurves: these are curves with the same degree and the same singularities but with non-homeomorphic complements. He also proved that the Alexander polynomial of a curve divides the Alexander polynomial of its link at infinity and the product of Alexander polynomials of the links of its singularities. We extend Libgober's definition to the symplectic case and prove that the divisibility relations also hold in this context. This is joint work with Hanine Awada. Ìý
 +Ìý
 +  Conan Leung (The Chinese AV¶ÌÊÓƵ of Hong Kong)Ìý
 +  14h30, Salle B217Ìý
 +  3d Mirror Symmetry is 2d Mirror SymmetryÌý
 +  Ìý
 +We introduce an approach to study 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors. Ìý
 +Ìý
 +  Sobhan Seyfaddini (ETH Zürich)Ìý
 +  14h30, Salle B217Ìý
 +  Closing Lemmas on Symplectic ManifoldsÌý
 +  Ìý
 +Given a diffeomorphism of a manifold, can one perturb it to create a periodic orbit passing through a specified region? This question, first raised in the 1960s, is known as the Closing Lemma. While the problem was resolved positively in C^1 regularity long ago, it remains largely open at higher levels of smoothness. Recent years have seen significant progress in the C^\infty setting, particularly for area-preserving maps on surfaces. In this talk, I will review these developments, highlighting works by Asaoka, Irie, Cristofaro-Gardiner, Edtmair, Hutchings, Prasad, and Zhang. I will also present some recent joint work with Cineli & Tanny and Mak & Smith, including partial results in higher dimensions.Ìý
 +Ìý
 +Ìý
 +Ìý
 +**2025, March 24, Monday, Université de Genève**Ìý
 +Ìý
 +  Lionel Lang (Gävle)Ìý
 +  14h00, Salle 01-15Ìý
 +  Logarithmic volumes of holes of hypersurfaces and tropicalization of periodsÌý
 +Ìý
 +Integrating the logaritmic volume form on well chosen discs bounded on hypersurfaces gives a local system of coordinates on the linear system of such hypersurfaces. Surprisingly, the same procedure gives global coordinates on the corresponding linear system of tropical hypersurfaces. In both the algebraic and tropical settings, the differential of these coordinate systems with respect to the coefficents of the defining equations are period matrices.  I want to discuss how this observation can be used to study the tropicalization of periods of hypersurfaces.Ìý
 +Ìý
 +  Johannes Rau (Universidad de los Andes)Ìý
 +  16h00, Salle 06-13Ìý
 +  Welschinger-Witt invariantsÌý
 +Ìý
 +The "quadratically enriched" invariants defined by Kass-Levine-Solomon-Wickelgren are obtained by counting rational curves over an arbitrary ground field and take values in the associated Witt-ring of quadratic forms. Specializing these values to rank and signature reproduces the corresponding Gromov-Witten and Welschinger invariants, respectively. In my talk, I want to introduce the concept of a Witt invariant which can be computed in terms of multiquadratic and multireal field extensions. We will see that Welschinger invariants give naturally rise to such an Witt invariant which in some cases (conjecturally always) coincides with the quadratically enriched invariants.Ìý
 +Ìý
 +**2024, December 6, Friday, Université de Genève**
  
   Jeffrey Hicks (Edinburgh)   Jeffrey Hicks (Edinburgh)
Ligne 10: Ligne 47:
  
 In this talk --- which will only use intuition, not techniques from symplectic geometry --- we give a candidate definition of the "Weinstein neighborhood" of a sheaf on an algebraic space, which extends the definition of an affine neighborhood of a point. We'll prove the existence of such a neighborhood for the structure sheaf of a hyperplane in projective space. Time permitting, we'll draw connections to tropical geometry and spaces of nonpositive curvature. In this talk --- which will only use intuition, not techniques from symplectic geometry --- we give a candidate definition of the "Weinstein neighborhood" of a sheaf on an algebraic space, which extends the definition of an affine neighborhood of a point. We'll prove the existence of such a neighborhood for the structure sheaf of a hyperplane in projective space. Time permitting, we'll draw connections to tropical geometry and spaces of nonpositive curvature.
 +
 +   Francesca Carocci (Roma)
 +   16h00, Salle 06-13
 +   Realizability of tropical maps via logarithmic geometry and curves singularities
 +
 +Abstract: In this talk I will explain the interpretation of Speyer well-spacedness condition for genus 1 realizability in terms of logarithmic deformation theory and curve singularities given by Ranganathan--Santos-Parker--Wise. I will then discuss how the same ideas can be used to approach the genus 2 realizability problem and the partial results obtained so far for this case.
  
  
symplectic.1733135405.txt.gz · Dernière modificationÌý: 2024/12/02 11:30 de g.m
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