fables
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Les deux révisions précédentesRévision précédenteProchaine révision | Révision précédenteProchaine révisionLes deux révisions suivantes | ||
fables [2023/02/28 16:53] – kalinin0 | fables [2023/04/20 21:28] – kalinin0 | ||
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====== Séminaire " | ====== Séminaire " | ||
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+ | FABLES GEOMETRIQUES MINICOURSE, April 24-27 | ||
+ | **Sergey Finashin (METU Ankara)** | ||
+ | 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 | ||
+ | |||
+ | |||
+ | **Strong Invariants in Real Enumerative Geometry** | ||
+ | |||
+ | Abstract: In the first lecture I will discuss a signed count of real lines on real projective hypersurfaces, | ||
+ | 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. | ||
+ | |||
+ | ---- | ||
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+ | 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, | ||
+ | |||
+ | ---- | ||
+ | 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. | ||
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Ligne 6: | Ligne 52: | ||
room 6-13 | room 6-13 | ||
- | **15h00 — Ali Ulaş Özgür Kişisel** | + | **15h00 — Ali Ulaş Özgür Kişisel |
**Expected measures of amoebas of random plane curves** | **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, | + | 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, |
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fables.txt · Dernière modification : 2023/12/05 11:54 de slavitya_gmail.com