Différences

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

--- fables [2023/03/17 14:22] – kalinin0
+++ fables [2023/12/05 11:54] (Version actuelle) – slavitya_gmail.com
@@ Ligne 1: / Ligne 1: @@
 ====== Séminaire "Fables Géométriques". ======
+----
+ 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