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
Fourier quasicrystals and their generalizations, zeros of Dirichlet series, other almost periodic objects, ICMS seminar talk by Sergey Favorov
A complex measure $\mu$ on a $d$-dimensional Euclidean space is a crystalline measure (CM) if it is the temperate distribution, its distributional Fourier transform $\hat\mu$ is also a measure, and supports of $\mu$ and $\hat\mu$ are discrete (locally finite); $\mu$ is a Fourier quasicrystal (FQ) if, in addition, $|\mu|$ and $|\hat\mu|$ are also temperate distributions. For example, if $\mu_0$ is the sum of the unit masses at all points with integer coordinates, then by Poisson's formula $\hat\mu_0=\mu_0$. Hence, $\mu_0$ is FQ. We show a theorem of Lev-Olevskii on a sufficient condition for trivialization of FQ. Then we discuss a simple condition for CM to be FQ and present CM that is not FQ. We recall the notion of an almost periodic function, introduce the notions of almost periodic measures, distributions, sets, and show their connections with CM. In paricular, we get various uniqueness theorems for FQ. Finally, we show the description of FQ with unit masses as zeros of exponential polynomials due to Olevskii and Ulanovskii, and discuss some generalizations to zeros of Dirichlet series and to measures in a horizontal strip of finite width.
Yukawa regulators in electrodynamics: Exact approach to the self-energy and anomalous g-factor, ICMS seminar talk by Miroslav Georgiev
In the present talk, we will discuss the prospect of electrodynamics in quantifying the self-interaction of a non-composite charged particle. We will demonstrate that under the consideration of unique to the particle Yukawa cut-offs the radial singularity in corresponding electromagnetic field potentials’ is removed allowing the classical theory to admit exact solutions for the particle’s self-energy and anomalous g-factor.
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.