An ICMS seminar talk by Mladen Dimitrov, University of Lille
Abstract: An amazing feature of the p-adic L-functions is their ability to live in families, thus their laws are governed by the geometry of p-adic eigenvarieties. In this lecture we will illustrate this philosophy through examples coming from classical modular forms and the Coleman-Mazur eigencurve.
In recent years several big advances enhance the field of complex geometry: Generalized geometries, Higgs and Langlands theory, Generalized Hodge theory, Hyperkaehler geometry. The goal of this conference is to consolidate and popularized new results in these directions. The event also seeks to provide an opportunity for young scholars from South-Eastern Europe to engage with cutting edge research in this area and to meet and interact with leading experts from around the world.
The initiative Women in Mathematics of South-Eastern Europe has been established in 2020 and has proven its worth in the last few years. Тhis is the fifth in a series of conferences of this initiative, the purpose of which is to make women in mathematics more visible, to help them share their ideas and scientific achievements and to communicate with each other not only scientifically but also empathetically and emotionally.
This small event is to celebrate the very successful collaboration between the institutes involved in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC), solidify our connections and expand even more the prosperous cooperation.
A seminar talk by Marta Pieropan, Utrecht University
Abstract: In joint work with Damaris Schindler we develop a new version of the hyperbola method for counting rational points of bounded height that generalizes the work of Blomer and Brüdern for products of projective spaces. The hyperbola method transforms a counting problem into an optimization problem on certain polytopes. For rational points on subvarieties of toric varieties, the polytopes have a geometric meaning that reflects Manin's conjecture, and the same holds for counts of Campana points of bounded height. I will present our results as well as some general heuristics.
From May 27 to 31, 2024, the International Conference Modern Methods in Nonlinear Elliptic and Parabolic PDE is being held in Plovdiv. Organizers of the event are the International Center for Mathematical Sciences at the Institute of Mathematics and Informatics with the financial support of the Simons Foundation.
The International Center for Mathematical Sciences – Sofia is organizing for a fourth consecutive year a meeting of young Bulgarian mathematicians from around the world. The conference will take place at the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences (IMI-BAS) on June 11 – 12, 2024.
The talk aims to review the progress in the study of higher rank P-and Q-polynomial association schemes, starting with the foundational concepts and recent advancements as outlined in the referenced papers. It will provide explicit examples of multivariate P-and Q-polynomial association schemes and explore the implications of these developments. The discussion will draw from multiple sources, including recent significant contributions by Bernard et al. and Crampé et al., and will conclude with speculations on future directions for research in this area.
This talk is based on the two joint papers with Hirotake Kurihara (Yamaguchi University), Da Zhao (East China University of Science and Technology) and Yan Zhu (Shanghai University for Science and Technology).
Classical amoebas serve as a tool to study algebraic varieties and as one of the entry points to tropical geometry. The original definition involves a logarithmic projection of a subvariety of a complex algebraic torus, which can be interpreted as forgetting the phase, i.e. the arguments of complex numbers. In group-theoretic terms, this projection map may be thought of as passing to the quotient by the maximal compact subgroup. Suppose one replaces the algebraic torus with a complex three-dimensional matrix group $PSL_2 \mathbb{C}$. In that case, the analogous projection naturally has a three-dimensional hyperbolic space as its target, and it still makes sense to consider images, i.e. hyperbolic amoebas, of complex algebraic varieties under this map. I will review some of the basic properties of hyperbolic amoebas, extending a fascinating interplay between complex and hyperbolic geometries.
In order to classify objects in singularity theory and algebraic geometry, we define invariants associated to varieties or germs of singularities and hope to have enough tools to compute them easily. From classical projective duality, for any variety X, we can define a dual variety X∗ and we call the class of X the degree of X∗. Plücker’s formula allows one to compute this class for plane curves with a certain set of nodes, cusps and tacnodes.
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