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

--- fables [2019/10/07 14:30] – weronika
+++ fables [2023/12/05 11:54] (Version actuelle) – slavitya_gmail.com
@@ Ligne 1: / Ligne 1: @@
 ====== Séminaire "Fables Géométriques". ======
-The normal starting time of this seminar is 16.30 on Monday.
+----
+ Friday, Dec 8, 14h30, Salle 06-13
+**Francesca Carocci (Genève)**
+**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.
+----
+  Monday, Nov 13, 15h, Salle 06-13
+**Francesca Carocci (Genève)**
+**What can we do with the Logarithmic Hilbert Scheme?**
+In 2020 Maulik-Ranganathan defined the Logarithmic Hilbert-Scheme, which is interesting for the enumerative geometry of 3-folds;  for example, it gives access to degeneration techniques in sheaf-theoretic approaches to curve counting.  If we go one step back and look at degree d curves in toric surfaces,  the construction of the log Hilbert scheme has as a main ingredient the secondary fan of a toric fan, though as  moduli space of tropical plane curves up to translation.
+I will try to explain some of the ideas of the construction, trying to put emphasis on the tropical aspects of the theory.
+The main goal of the talk would be to understand if this theory gives rise to some interesting questions and the relation of such questions with tropical geometry.
+----
+  May 22, salle 6-13, 15h
+**Oleg Viro (Stony Brook)**
+**Simplest numerical invariants for some kinds of curves**
+In the 90s, Arnold introduced several numerical characteristics of
+generic plane curves via axiomatic approach based on behavior of curves
+under "perestroikas". Soon explicit formulas for the invariants have
+been invented. The formulas have disclosed unexpected aspects of nature
+of the invariants and suggested various new objects to study, like real
+algebraic curves or circles inscribed in a generic plane curve.
+----
+**FABLES GEOMETRIQUES MINICOURSE, April 24-27**
+  Lecture 1, Monday, April 24, 15h, room 6-13
+  Lecture 2, Tuesday, April 25, 13h, Room 1-07
+  Lecture 3, Thursday, April 27, 16h15, Room 1-15
+**Sergey Finashin (METU Ankara)**
+**Strong Invariants in Real Enumerative Geometry**
+In the first lecture I will discuss a signed count of real lines on real projective hypersurfaces, which is independent of the choice of real structures and in that sense is “strong invariant”. The simplest examples: a signed count of real lines on a real cubic surface gives 3, while a similar count on a real quintic 3-fold gives 15. In the other lectures I will stick to the case of real del Pezzo surfaces and discuss a generalization of the signed count of lines to a signed count of rational curves (involving some combinations of the Welschinger numbers).
+All the results are joint with V.Kharlamov.
+----
+  Monday, April 3, 2023
+  room 6-13
+**15h00 — Alexander Bobenko (TU Berlin)**
+**Discrete conformal mappings, ideal hyperbolic polyhedra, and Ronkin function**
+The general idea of discrete differential geometry is to find and investigate discrete models that exhibit properties and structures characteristic for the corresponding smooth geometric objects. We focus on a discrete notion of conformal equivalence of polyhedral metrics. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by scale factors associated with the vertices. This simple definition leads to a surprisingly rich theory. We review connections between conformal geometry of triangulated surfaces, the geometry of ideal hyperbolic polyhedra and discrete uniformization of Riemann surfaces. Surprisingly, variational description of discrete conformal mappings is given by Ronkin function on amoeba with three ends. Applications in geometry processing and computer graphics will be demonstrated.
+----
+  Monday, March 27, 2023
+  room 6-13
+**16h00 — Sebastian Haney (Columbia U)**
+**Mirror Lagrangians to lines in P^3**
+We discuss work in progress in which we construct, for any tropical curve in $R^n$ with vertices of valence at most $4$, a Lagrangian submanifold of $(C^*)^n$ whose moment map projection is a tropical amoeba. These Lagrangians will have singular points modeled on the Harvey-Lawson cone over a $2$-torus. We also consider a certain $4$-valent tropical curve in $R^3$, for which we can modify the singular Lagrangian lift to obtain a cleanly immersed Lagrangian. The objects of the wrapped Fukaya category supported on this Lagrangian correspond, under mirror symmetry, to lines in $CP^3$. If time permits, we will explain how to use functors induced by Lagrangian correspondences to see this mirror relation.
+----
+  Monday, March 20, 2023
+  room 6-13
+**16h00 — Ilia Itenberg (Sorbonne)**
+**Maximal real algebraic hypersurfaces of projective spaces**
+The talk is devoted to a combinatorial patchworking construction of maximal (in the sense of the generalized Harnack inequality) real algebraic hypersurfaces in real projective spaces (joint work with Oleg Viro).
+During the talk, we will mainly concentrate on the construction of a maximal quintic hypersurface in the 4-dimensional real projective space.
+----
+  Monday, March 6, 2023
+  room 6-13
+**15h00 — Ali Ulaş Özgür Kişisel (METU, Ankara)**
+**Expected measures of amoebas of random plane curves**
+There are several natural measures that one can place on the amoeba of an algebraic curve in the complex projective plane. Passare and Rullgård prove that the total mass of the Lebesgue measure on the amoeba of a degree $d$ curve is bounded above by $π^{2} d^{2} / 2$, by comparing it to another Monge-Ampère type measure, which is dual to the usual measure on the Newton polytope of the defining polynomial via the Legendre transform. Mikhalkin generalizes this upper bound to half-dimensional complete intersections in higher dimensions, by considering another measure supported on their amoebas; their multivolume. The goal of this talk will be to discuss these measures in the setting of random plane curves. In particular, I’ll first present our results with Bayraktar, showing that the expected multiarea of the amoeba of a random Kostlan degree $d$ curve is equal to $π^2 d$. For Lebesgue measure, it turns out that the expected asymptotics are much lower: I’ll describe our results with Welschinger, showing that the expected Lebesgue area of the amoeba of a random Kostlan degree $d$ curve is of the order $(\log d)^2.$
+----
+  Monday, February 27, 2023
+  room 6-13
+**15h00 — Evgeni Abakoumov (Paris/Eiffel U)**
+**Chui's conjecture аnd rational approximation**
+C. K. Chui conjectured in 1971 that the average gravitaional field strength in the unit disk due to unit point masses on its boundary was the smallest when these point masses were equidistributed on the circle. We will present an elementary solution to some weighted versions of this problem, and discuss related questions concerning approximation of holomorphic functions by simple partial fractions. This is joint work with A. Borichev and K. Fedorovskiy.
+**16h00 — Ferit Ozturk (Istanbul/Bosphorus U and Budapest/Renyi Inst)**
+**Every real 3-manifold admits a real contact structure**
+We survey our results regarding real contact 3-manifolds and present our result in the title.
+A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure.
+A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with respect to the real structure.
+The standard examples of real contact 3-manifolds are link manifolds of isolated, real analytic surface singularities.
+We show that every real contact 3-manifold can be obtained via contact surgery along invariant knots starting from the standard real contact 3-sphere.
+As a corollary we show that any oriented overtwisted contact structure on an integer homology real 3-sphere can be isotoped to be real.
+----
+  Monday, February 6, 2023
+:00, room 6-13
+**Sergey Finashin (Ankara)**
+**“Affine Real Cubic Surfaces”**
+Abstract: (A joint work with V.Kharlamov) We prove that the space of
+affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other via wall-crossing.
+----
+  Thursday, June 16, 2022
+:00, room 1-07
+**Prof.  Yakov Eliashberg (Stanford)**
+**“Topology of spaces of Legendrian knots via Algebraic K-theory”**
+Abstract: The highly non-trivial stable homotopy groups of the Waldhausen’s
+h-cobordism space inject into the homotopy groups of spaces of appropriate Legendrian submanifolds. For instance,  there is  a  homotopically non-trivial 2-parametric family of Legendrian unknots in ${\mathbb R}^{2n+1}$ for a sufficiently large $n$. This is a joint work with Thomas Kragh.
+----
+  Fri 17.12.2021, 13h30, room 6-13
+  Andras Szenes
+**Diagonal bases and wall-crossings in moduli spaces of vector bundle**
+The idea  of the calculation of the Hilbert function of the moduli spaces of vector bundles on Riemann surfaces goes back to the works of Michael Thaddeus in the early 90’s.
+I describe joint work with Olga Trapeznikova where this plan is carried out in detail, which uses only basic tools of Geometric Invariant Theory and a combinatorial/analytic device introduced by myself: the diagonal basis of hyperplane arrangements.
+----
+  Nov 1, 16h15. Room 06-13
+  Vasily Golyshev (Moscow, Bures-sur-Yvette)
+**Markov numbers in number theory, topology, algebraic geometry, and differential equations**
+I will explain how the Markov numbers arise in different mathematical
+disciplines, and sketch the links. A recent contribution will be discussed, too.
+----
+, Wednesday, May 20, 16:00 (CEST), Virtual seminar, Lionel Lang (Stockholm University)
+https://unige.zoom.us/j/5928729514
+Meeting ID: 592 872 9514  Password: (the number of lines on a cubic surface)
+**Co-amoebas, dimers and vanishing cycles**
+In this joint work in progress with J. Forsgård, we study the topology of maps P:(\C*)^2 \to \C given by Laurent polynomials P(z,w).
+For specific P, we observed that the topology of the corresponding map can be described in terms of the co-amoeba of a generic fiber. When the latter co-amoeba is maximal, it contains a dimer (a particularly nice graph) whose fundamental cycles corresponds to the vanishing cycles of the map P. For general P, the existence of maximal co-amoebas is widely open. In the meantime, we can bypass co-amoebas, going directly to dimers using a construction of Goncharov-Kenyon and obtain a virtual correspondence between fundamental cycles and vanishing cycles.
+In this talk, we will discuss how this (virtual) correspondence can be used to compute the monodromy of the map P.
+----
+, Tuesday, April 7, 17:00, Virtual seminar (EDGE seminar) Grigory Mikhalkin (Geneva)
+https://zoom.us/j/870554816?pwd=bERmR0ZQTitYNXJ1aFZLckxzeXZJZz09
+Meeting ID: 870 554 816 Password: 014504
+**Area in real K3-surfaces**
+Real locus of a K3-surfaces is a multicomponent topological surface. The canonical class provides an area form on these components (well defined up to multiplication by a scalar). In the talk we'll explore inequalities on total areas of different components as well a link between such inequalities and a class of real algebraic curves called simple Harnack curves. Based on a joint work with Ilia Itenberg.
+----
+, Monday, March 31, 17:00, Virtual seminar, Vladimir Fock (Strasbourg)
+https://unige.zoom.us/j/737573471
+Meeting ID: 737 573 471
+**Higher measured laminations and tropical curves**
+We shall define a notion of a higher lamination - a graph embedded
+into a Riemann surface with edges coloured by generators of an affine
+Weyl group. This notion generalises the notion of the ordinary
+integral measured lamination and on the other hand of a tropical
+curve and can be constructed out of a integral Lagrangian submanifold
+of the cotangent bundle.
+----
+, Monday, March 16, 16:30, Battelle, Alexander Veselov (Loughborough University)[POSTPONED]
+**On integrability, geometrization and knots**
+I will start with a short review of Liouville integrability in relation with Thurston’s geometrization programme,
+using as the main example the geodesic flows on the 3-folds with SL(2,R)-geometry.
+A particular case of such 3-folds the modular quotient SL(2,R)/SL(2,Z), which is known, after Quillen, to be equivalent to the complement in 3-sphere of the trefoil knot. I will show that remarkable results of Ghys about modular and Lorenz knots can be naturally extended to the integrable region, where these knots are replaced by the cable knots of trefoil.
+The talk is partly based on a recent joint work with Alexey Bolsinov and Yiru Ye.
+----
+, Monday, February 17, 16:30, Battelle, Karim Adiprasito
+  (University of Copenhagen, Hebrew University of Jerusalem)
+** Algebraic geometry of the sphere at infinity, polyhedral de Rham theory and L^2 vanishing conjectures **
+I will discuss a conjecture of Singer concerning the vanishing of L^2 cohomology on non-positively curved manifolds, and relate it to Hodge theory on a Hilbert space that arises as the limit of Chow rings of certain complex varieties.
+----
+, Friday, December 6, 15:00, Battelle, Tomasz Pelka (UniBe)
+** Q-homology planes satisfying the Negativity Conjecture **
+A smooth complex algebraic surface S is called a Q-homology plane if H_i(S,Q)=0 for i>0. This holds for example if S is a complement of a rational cuspidal curve in P^2. The geometry of such S is understood unless S is of log general type, in which case the log MMP applied to the log smooth completion (X,D) of S is insufficient. The idea of K. Palka was to study the pair (X,(1/2)D) instead. This approach gives much stronger constraints on the shape of D, and leads to the Negativity Conjecture, which asserts that the Kodaira dimension of K_X+(1/2)D is negative. It is a natural generalization e.g. of the Coolidge-Nagata conjecture about rational cuspidal curves, which was recently proved using these methods by M. Koras and K. Palka.
+If this conjecture holds, all Q-homology planes of log general type can be classified. It turns out that, as expected by tom Dieck and Petrie, they are arranged in finitely many discrete families, each obtainable in a uniform way from certain arrangements of lines and conics on P^2. As a consequence, they all satisfy the Strong Rigidity Conjecture of Flenner and Zaidenberg; and their automorphism groups are subgroups of S_3. To illustrate this surprising rigidity, I will show how to construct all rational cuspidal curves (with complements of log general type, satisfying the Negativity Conjecture) inductively, by iterating quadratic Cremona maps. This construction in particular shows that any such curve is uniquely determined, up to a projective equivalence, by the topology of its singular points.
+----
+, Monday, November 25, 16:30, Battelle, Felix Schlenk (UniNe)
+** (Real) Lagrangian submanifolds **
+We start with describing how Lagrangian submanifolds of symplectic
+manifolds naturally appear in many ways: In celestial mechanics, integrable systems, symplectic geometry, and algebraic geometry.
+We then look at real Lagrangians, namely those which are the fixed point set
+of an anti-symplectic involution. How special is the property of being real?
+While many of the examples discussed above are real, we explain why the
+central fibres in toric symplectic manifolds are real only if the moment polytope
+is centrally symmetric.
+The talk is based on work of and with Joé Brendel, Yuri Chekanov, and Joontae Kim.
+----
+, Friday, November 8, 14:00, Battelle, Johannes Rau (University of Tübingen)
+** The dimension of an amoeba **
+Amoebas are projections of algebraic varieties in logarithmic coordinates and were originally introduced by Gelfand, Kapranov and Zelevinsky in their influential book. Based on some computation, Nisse and Sottile formulated some questions concerning the dimension of amoebas. In a joint work with Jan Draisma and Chi Ho Yuen, we answer these questions by providing a general formula that computes the dimension of amoebas. If time permits, we also discuss the consequences of this formula for matroidal fans.
+----
 , Monday, November 4, 16.30, Battelle, Pierrick Bousseau (ETH Zurich)
-Title: TBA
+** Quasimodular forms from Betti numbers**
+This talk will be about refined curve counting on local P2, the noncompact Calabi-Yau 3-fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu.
 ----