ICMS Seminar
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics.
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics. The seminar hosts scientific reports by collaborators and visitors of the ICMS, as well as colloquium-style lectures by invited speakers. The interdisciplinary features of the ICMS are reflected in the variety of topics covered in the seminar, ranging in algebraic and differential geometry, number theory, category theory, combinatorics, representation theory, mathematical physics, algebraic coding theory, etc. The venue is open to a wide audience, and the lectures are followed by time for interaction and discussion.
Seminar issues
Regularized Quantum Motion in a Bounded Set: Hilbertian Aspects, talk by Jean-Pierre Gazeau
In this talk, we demonstrate that essential self-adjointness can be restored by symmetrically weighting the momentum operator with a positive bounded function that approximates the indicator function of the given interval. This weighted momentum operator arises naturally from a similarly weighted classical momentum through the Weyl-Heisenberg covariant integral quantization of functions or distributions.
Generalized integral points and strong approximation, talk by Boaz Moerman
A seminar talk by Boaz Moerman, Utrecht University
Abstract: The Chinese remainder theorem states that given coprime integers p_1, ..., p_n and integers a_1, ..., a_n, we can always find an integer m such that m ~ a_i mod p_i for all i. Similarly given distinct numbers x_1,..., x_n and y_1, ..., y_n we can find a polynomial f such that f(x_i)=y_i. These statements are two instances of strong approximation for the affine line (over the integers Z and the polynomials k[x] over a field k). In this talk we will consider when an analogue of this holds for special subsets of Z and k[x], such as squarefree integers or polynomials without simple roots, and different varieties. We give a precise description for which subsets this holds on a toric variety.
P-adic L-functions and the geometry of the Eigencurve, talk by Mladen Dimitrov
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.
Rational points and Campana points on toric varieties and their subvarieties, talk by Marta Pieropan
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.
Multivariate P- and Q-polynomial association schemes, talk by Eiichi Bannai
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).
