Preisträger 2021

Preisverleihung und Vorträge

Aus gesundheitlichen Gründen fanden diese Veranstaltungen nicht statt.

Symposium

Freitag, 29. Oktober 2021

Hyperbolicity and non-reductive intersection theory

externe Seite Gergely Bérczi (Aarhus)

Abstract: Non-reductive reparametrisation group actions play a central role in hyperbolicity questions due to the strategy developed by Demailly, Siu et al. to study degeneracy of entire curves. We explain how this strategy, combined with intersection theory of non-reductive geometric invariant theory-type quotients led to the recent proof of the Green-Griffiths-Lang and Kobayashi hyperbolicity conjectures for generic projective hypersurfaces with polynomial degree.

Singular Kähler-Einstein metrics

externe Seite Eleonora Di Nezza (Palaiseau)

Abstract: In the last 50 years the study of the Monge-Ampère operator has played a central role in order to solve geometric problems, such as the existence of special metrics (e.g. Kähler-Einstein, cscK) on a compact Kähler manifold. In this talk I am going to present
some recent developments in “singular” settings: we will work with a singular variety and we look for singular metrics. The talk is based on a series of joint papers with Támas Darvas and Chinh Lu.

Two applications of two foundational results by J.-P. Demailly

externe Seite Simone Diverio (Rome)

Abstract: To misquote the Peter Parker principle “With great power comes great responsibility”, with great theorems come interesting consequences, even several decades after. During the 80’s, when he still was in his late twenties, J.-P. Demailly proved several profound and fundamental theorems, among which we want to focus here on his L^2 estimates for the d-bar operator, and his vanishing theorems for tensor powers of ample vector bundles. We shall discuss two very recent applications of these two results, respectively in collaboration with S. Boucksom, B. Cadorel, H. Guenancia, and with F. Fagioli. The first is a confirmation of Lang’s conjecture about subvarieties of Kobayashi hyperbolic manifolds in the special case of quotients of bounded non necessarily homogeneous domains. The second is a partial proof of Griffiths’ conjecture about positivity of characteristic forms of positive holomorphic Hermitian vector bundles.