Nikolaos Tsakanikas (EPF Lausanne)
Applications of Zariski decompositions abstract
Abstract:
The Minimal Model Program (MMP) plays a central role in the classification theory of projective varieties. In this talk I will discuss recent progress towards the existence of minimal models, which is one of the main open problems in the MMP. In particular, I will explain the close relationship between the existence of minimal models and the existence of so-called weak Zariski decompositions, focusing mainly on applications of the latter. This talk is based on joint works with Xiaowei Jiang, Vladimir Lazić and Lingyao Xie.
13:15 • EPF Lausanne, Salle MA A3 30
Alexander Varchenko (University of North Carolina, Chapel Hill)
Polynomial solutions of KZ equations modulo an integer abstract
Abstract:
I will review the construction of polynomial solutions of KZ equations modulo an integer and the properties of the solutions, in particular, their p-adic limit.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Carlo Pagano (Concordia University, Montreal)
Abstract:
A conjecture of Chowla postulates that no L-function of Dirichlet characters over the rationals vanishes at s=1/2. Soundararajan has proved non-vanishing for a positive proportion of quadratic characters. Over function fields Li has discovered that Chowla\'s conjecture fails for infinitely many distinct quadratic characters. However, on the basis of the Katz--Sarnak heuristics, it is still widely believed that one should have non-vanishing for 100% of the characters in natural families (such as the family of quadratic characters). Works of Bui--Florea, David--Florea--Lalin, Ellenberg--Li--Shusterman, among others, provided evidence giving a positive proportion of non-vanishing in several such families. I will present an upcoming joint work with Peter Koymans and Mark Shusterman, where we prove that for each fixed q congruent to 3 modulo 4 one has 100% non-vanishing in the family of imaginary quadratic function fields.
17:00 • Universität Basel, online Seminar