Embedded Files
The speakers and the abstracts of the talks are listed below in alphabetical order.
Samir Canning (ETHZ)
Samir Canning (ETHZ)
Moduli spaces of curves with polynomial point counts
Title: Moduli spaces of curves with polynomial point counts
Abstract: I will explain some recent progress on counting curves of a fixed genus over finite fields. The path to point counting goes through the cohomology of the moduli space of stable curves and the Weil conjectures. This is joint work with Larson, Payne and Willwacher.
Daniele Faenzi (Dijon)
Daniele Faenzi (Dijon)
Title: Logarithmic derivations along discriminant divisors.
Title: Logarithmic derivations along discriminant divisors.
Abstract: The sheaf of logarithmic derivations tangent to a divisor is a useful tool in the study of singularities, particularly for configurations of hyperplanes with many symmetries. We will examine some of its properties, such as freeness and stability, and then its connection with projective duality. We will focus on the study of this sheaf in the case of divisors invariant under the action of an algebraic group, in particular discriminants of certain classes of representations, starting from the adjoint representation of a simple algebraic group and moving to stable polar representations and theta-groups.
Project in collaboration with Vladimiro Benedetti, Simone Marchesi, Masahiko Yoshinaga.
Dongchen Jiao (Basel)
Existence of complements for foliations
Dongchen Jiao (Basel)
Existence of complements for foliations
Title: Existence of complements for foliations
Abstract: The notion of complements, a distinguished class of global sections of the anti-canonical sheaf of a variety, was introduced by Shokurov. Subsequently, the theory of complements was substantially developed and has come to play a central role in birational geometry. Birkar established the existence of bounded complements for varieties of Fano type in fixed dimension. In higher dimensions, recent advances in the development of the Minimal Model Program (MMP) for foliated varieties, in particular on algebraically integrable foliations allow to investigate the existence of (bounded) complements in the foliated setting. As opposed to complements for varieties, even the existence of Q-complements due to the general failure of Bertini-type results is by no means trivial. we show the existence of Q-complements for algebraically integrable log-Fano foliations on klt varieties. This is a joint work with Y. Chen and P. Voegtli.
Léo Navarro Chafloque (EPFL)
Title Perfectoidizations of finite algebras over a perfectoid ring
Léo Navarro Chafloque (EPFL)
Title Perfectoidizations of finite algebras over a perfectoid ring
Title: Perfectoidizations of finite algebras over a perfectoid ring
Abstract: In characteristic p, an important notion in algebra and geometry is the notion of perfection of a ring. In mixed charateristic, a more complicated analogue exists, the perfectoidization, which was introduced by Bhatt and Scholze in tandem with prismatic cohomology. This notion is way more complicated; we will explain how one can understand nonetheless some examples of perfectoidization of finite algebras over a perfectoid ring. Some of the work exposed is joint with Ryo Ishizuka.
Isabel Stenger (Hannover)
Beyond the Morrison-Kawamata cone conjecture
Isabel Stenger (Hannover)
Beyond the Morrison-Kawamata cone conjecture
Title: Beyond the Morrison-Kawamata cone conjecture
Abstract: The birational geometry of a projective variety is closely intertwined with the structure of its cones of divisors, in particular the nef cone and the movable cone. The Morrison–Kawamata cone conjecture predicts that the cones of effective nef divisors and effective movable divisors of a Calabi–Yau manifold are rational polyhedral up to the action of suitable automorphism groups. So far, the effective cone itself has played only a secondary role in this conjectural picture. We formulate an effective cone conjecture and show that, assuming the existence of good minimal models in dimension dim X, it is equivalent to the movable cone conjecture. As an application, we show that the movable cone conjecture holds unconditionally for the smooth Calabi–Yau threefolds introduced by Schoen.
This is joint work with Cécile Gachet, Hsueh-Yung Lin and Long Wang.
Immanuel van Santen (Bern)
Symmetric (border) subrank
Immanuel van Santen (Bern)
Symmetric (border) subrank
Title: Symmetric (border) subrank
Abstract: This talk is based on joint work with Benjamin Biaggi, Jan Draisma and Koen de Nooij.
Let f be a homogeneous polynomial of degree d. For each integer r, we consider the set L_f^r of degree d polynomials obtained by substituting the variables of f with linear forms in variables x_1, …, x_r. The symmetric (border) subrank of f is the largest r such that sum_i x_i^d lies in (the closure of) L_f^r.
I will first discuss the asymptotic behaviour of the symmetric (border) subrank of a generic f as n tends to infinity. I will then turn to low-degree cases, where the symmetric subrank and border subrank coincide. In this setting, classical invariant theory allows us to show that plane (line) sections of cubic (quartic) projective hypersurfaces realize all smooth isomorphism classes.
Henrik Wehrheim (Neuchâtel)
Title: Sarkisov links starting with the blow up of a smooth surface of P^4 of small degree.
Henrik Wehrheim (Neuchâtel)
Title: Sarkisov links starting with the blow up of a smooth surface of P^4 of small degree.
Title: Sarkisov links starting with the blow up of a smooth surface of P^4 of small degree.
Abstract: The study of blowups along points in P_C^2 and their Sarkisov links is complete and there are already a lot of results on blowups along points and curves in P_C^k3, the case of dimension 4 has not been studied as extensively yet. We focus here on the blowups along surfaces as they are in a sense the new case of dimension 4. So using classifications of smooth surfaces of small degree (< 9) in P_C^4 we can construct one by one the links starting from their blowups. This gives us examples for behaviours of Sarkisov links in fourfolds.
Page updated
Google Sites
Report abuse