Différences

Ci-dessous, les différences entre deux révisions de la page.

--- start [2022/09/16 15:27] – kalinin0
+++ start [2024/03/12 13:13] (Version actuelle) – slavitya_gmail.com
@@ Ligne 5: / Ligne 5: @@
 ----
-PhD graduated: Kristin Shaw (December 2011), Lionel Lang (December 2014), [[http://mathcenter.spb.ru/nikaan/|Nikita Kalinin]] (December 2015), [[Mikhail Shkolnikov|Mikhail Shkolnikov]] (June 2017),
+PhD graduated: Kristin Shaw (December 2011), Lionel Lang (December 2014), [[https://scholar.google.com/citations?user=HFzzTtkAAAAJ|Nikita Kalinin]] (December 2015), [[Mikhail Shkolnikov|Mikhail Shkolnikov]] (June 2017),
 Johannes Josi (February 2018).
-Current members:Thomas Blomme, Weronika Czerniawska, [[Grigory Mikhalkin|Grigory Mikhalkin]], [[alina|Alina Pavlikova]], Mikhail Pirogov.
+Current members: Thomas Blomme, Francesca Carocci, Slava Goncharov, [[Grigory Mikhalkin|Grigory Mikhalkin]], Antoine Toussaint.
-Alumni: Ivan Bazhov, Johan Bjorklund, Rémi Crétois, Yi-Ning Hsiao, Jens Forsgard, Maxim Karev, Ilya Karzhemanov, Sergei Lanzat, Michele Nesci, Johannes Rau, Arthur Renaudineau.
+Alumni: Ivan Bazhov, Johan Bjorklund, Rémi Crétois, Weronika Czerniawska, Yi-Ning Hsiao, Jens Forsgard, Maxim Karev, Ilya Karzhemanov, Sergei Lanzat, Michele Nesci, Alina Pavlikova, Mikhail Pirogov, Johannes Rau, Arthur Renaudineau.
 We organize several seminars:
@@ Ligne 16: / Ligne 16: @@
 [[fables|Séminaire "Fables Géométriques"]].
-pre-2017 [[batelle|Battelle Seminar]] and
+pre-2017 (historical) [[batelle|Battelle Seminar]] and
 [[working|Tropical working group Seminar]].
@@ Ligne 27: / Ligne 27: @@
 ----
 ====== Seminars and conferences ======
+----
---------------
+  Prof. Ilia Itenberg (Sorbonne University), Friday, March 15, SM 01-05, 15h15-17h
-**2022, September 27, Tuesday, Université de Neuchâtel**
-  Richard Hind (University of Notre Dame)
-  Obstructing Lagrangian isotopies
+"Basic algebra and algebraic geometry special talk:
-  Room B107, 14:00
+Real plane sextic curves without real singular points"
+We will start with a brief introduction to topology of real algebraic curves,
+and then will discuss in more details the case of curves of degree 6 in the real projective plane.
+We will prove that the equisingular deformation type of a simple real plane sextic curve
+with smooth real part is determined by its real homological type, that is, the polarization, exceptional divisors,
+and real structure recorded in the homology of the covering K3-surface (this is a joint work with Alex Degtyarev).
+----
+  Alexander Bobenko (TU Berlin), Feb 16, 2024, at 14h30, Salle 01-05
+"Dimers and M-curves"
+We develop a general approach to dimer models analogous to Krichever’s scheme in the theory of integrable systems. This leads to dimer models on doubly periodic bipartite graphs with quasiperiodic positive weights.
+This generalization from Harnack curves to general M-curves leads to transparent algebro-geometric structures. In particular explicit formulas for the Ronkin function and surface tension as integrals of meromorphic differentials on M-curves are obtained. Based on Schottky uniformizations of Riemann surfaces we compute the weights and dimer configurations. The computational results are in complete agreement with the theoretical predictions. Also relation to discrete conformal mappings and to hyperbolic polyhedra is explained. This is a joint work with N. Bobenko and Yu. Suris.
+----
+  Francesca Carocci (Genève), Dec 8, 14h30, Salle 06-13
+"Degenerations of Limit linear series"
+Maps to projective space are given by basepoint-free linear series, thus these are key to understanding the extrinsic geometry of algebraic curves.
+How does a linear series degenerate when the underlying curve degenerates and becomes nodal?
+Eisenbud and Harris gave a satisfactory answer to this question when the nodal curve is of compact type. Eisenbud-Harris's theory of limit linear series gives proofs via degenerations  of many foundational results in Brill--Noether theory, and it is powerful enough to answer several  birational geometry questions on the moduli space of curves.
+I will report on a joint work in progress with Lucaq Battistella and Jonathan Wise, in which we review this question from a moduli-theoretic and logarithmic perspective. The logarithmic prospective helps understanding the rich polyhedral and combinatorial structures underlying degenerations of linear series. These are linked with matroids and Bruhat-Titts buildings.
+----
+  Diego MATESSI (Milano), Dec 4, 15h, Salle 06-13
+"Tropical mirror symmetry and real Calabi-Yaus"
+I will present some work in progress jont with Arthur Renaudineau.  The goal is to understand the topology of real Calabi-Yaus by combining the Renaudineau-Shaw spectral sequence with mirror symmetry.  We will consider mirror pairs of Calabi-Yau hypersurfaces X and X' in toric varieties associated to dual reflexive polytopes. The first step is to prove an isomorphism between tropical homology groups of X and X', reproducing the famous mirror symmetry exchange in hodge numbers. We then expect that the boundary maps in the Renaudineau-Shaw spectral sequence, computing the homology of the real Calabi-Yaus, can be interpreted, on the mirror side, using classical operations on homology.
+----
+  Thomas Blomme, université de Genève, Thursday, Nov 9, 16h15, Room 1-15.
+"Gromov-Witten invariants of bielliptic surfaces"
+Bielliptic surfaces were classified by Bagnera & de Francis more than a century ago. They form a family spread into seven subfamilies of the Kodaira-Enriques surface classification which have nearly trivial canonical class in the sense that it is non-zero, but torsion. Thus, the virtual dimension of the moduli space of curves only depends on the genus, and contrarily to abelian and K3 surfaces, it yields non-zero invariants. In this talk we'll focus on some techniques to compute GW invariants of these surfaces along with some regularity properties.
+----
+  Antoine Toussaint, université de Genève, Monday, Oct 23, at 15h, Salle 06-13
-**Abstract:**
+"Real Structures of Phase Tropical Surfaces"
+Phase tropical surfaces can appear as a limit of a 1-parameter family of smooth complex algebraic surfaces. A phase tropical surface admits a stratified fibration over a smooth tropical surface. We study the real structures compatible with this fibration and give a description in terms of tropical cohomology. As an application, we deduce combinatorial criteria for the type of a real structure of a phase tropical surface. Time permitting, we will also discuss the connection with Renaudineau and Shaw's spectral sequence and Kalinin's spectral sequence.
+----
+  Ozgur CEYHAN (University of Luxembourg), Monday, Oct 16, at 15h, Salle 06-13
+"Complexities in backpropagation and tropicalization in neural networks"
+The backpropagation algorithm and its variations are the primary training method of multi-layered neural networks. The backpropagation is a recursive gradient descent technique that works on large matrices.
+This talk explores backpropagation via tropical linear algebra and introduces multi-layered tropical neural networks as universal approximators. After giving a tropical reformulation of the backpropagation algorithm, we verify the algorithmic complexity is substantially lower than the usual backpropagation as the tropical arithmetic is free of the complexity of usual multiplication.
+----
+  Gurvan Mével (Université de Nantes), Wednesday, Oct 18, at 14h15, Salle 06-13
-I will describe some obstructions to the existence of Lagrangian tori in subsets of Euclidean space, and also to isotopies between the tori. The obstructions come from holomorphic curves and In simple situations are sharp. As a consequence we can derive obstructions to certain 4 dimensional symplectic embeddings, which turn out not to be especially strong, but the analysis does lead to precise statements about stabilized ellipsoid embeddings. Results are taken from joint works with Emmanuel Opshtein, Jun Zhang and Kyler Siegel and Dan Cristofaro-Gardiner.
+“Universal polynomials for coefficients of tropical refined invariant in genus 0”
-  Joé Brendel (Université de Neuchâtel and Tel Aviv University)
+In enumerative geometry, some numbers of curves on surfaces are known to behave polynomially when the cogenus is fixed and the linear system varies, whereas it grows more than exponentially fast when the genus is fixed. In the first case, Göttsche's conjecture expresses the generating series of these numbers in terms of universal polynomials.
-  Lagrangian tori in S^2 x S^2
-  Room E213, 16:00
-**Abstract:**
+Tropical refined invariants are polynomials resulting of a weird way of counting curves, but linked with the previous enumerations. When the genus is fixed, Brugallé and Jaramillo-Puentes proved that some coefficients of these polynomials behave polynomially, bringing back a Göttsche's conjecture in a dual and refined setting. In this talk we will investigate the existence of universal polynomials for these coefficients.
-There is an obvious family of Lagrangian tori in $S^2 \times S^2$, namely those obtained as a product of circles in the factors. We discuss the classification of such product tori up to symplectomorphisms and note that the non-monotone case is qualitatively very different from the monotone one. In the proof, we use a symmetric version of McDuff's probes. The resulting classification can be used to tackle many related questions: Which of the above tori are the image of a product torus in a ball under a Darboux embedding? What is the Hamiltonian monodromy group of the product tori? How many disjoint copies (up to Hamiltonian isotopy) of a given product torus can be packed into the ambient space? Why does the Lagrangian analogue of the flux conjecture fail so badly? If time permits we will say something about exotic tori, i.e. tori which are not symplectomorphic to product tori. This is partially based on joint work with Joontae Kim.
 [[symplectic| seminar page]]
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-If you want to register, say me (Misha Shkolnikov). You should be approved user to edit pages.
+You should be approved user to edit pages.
 You can write here something. (Create a small web page about you, write about you interests, explain tropical philosophy of our group, upload articles etc).