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

--- fables [2023/04/20 21:28] – kalinin0
+++ fables [2023/12/05 11:54] (Version actuelle) – slavitya_gmail.com
@@ Ligne 3: / Ligne 3: @@
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-  FABLES GEOMETRIQUES MINICOURSE, April 24-27
+ Friday, Dec 8, 14h30, Salle 06-13
-  **Sergey Finashin (METU Ankara)**
-  Lecture 1, Monday, April 24, 15h, room 6-13
-  Lecture 2, Tuesday, April 25, 13h, Room 1-07
+**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**
-Abstract: 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
+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).
-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.