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

--- fables [2023/03/23 03:24] – kalinin0
+++ fables [2023/05/17 11:01] – kalinin0
@@ Ligne 1: / Ligne 1: @@
 ====== Séminaire "Fables Géométriques". ======
+----
+  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
@@ Ligne 8: / Ligne 48: @@
 **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.
+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