New Program of the ICMS: Algebraic, Computational, and Topological Perspectives on Complexity
The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) is happy to announce that based on a strong selection process done by the Recruitment committee, the Advisory Board of ICMS-Sofia approved Prof. Ernesto Lupercio as a Chair of a new program Algebraic, Computational, and Topological Perspectives on Complexity
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.
International Educational Workshop on the Theory of Atoms: Foundations, Advances, and Future Directions
From December 16 to 19, 2024, we hosted an educational workshop on the Theory of Atoms. The goal of this workshop was to explain the foundations of the new theory of atoms, introduced recently by L. Katzarkov, M. Kontsevich, T. Pantev and T. Yu. The workshop attracted over 40 researchers from around the world, including Austria, Belgium, Brazil, Colombia, France, Germany, Hungary, India, Mexico, South Korea, Switzerland, and the USA, underscoring its global significance. The event marked the launch of a new 5-year program on the Theory of Atoms, supported by a grant from the Simons Foundation and funding from the Ministry of Education and Science of the Republic of Bulgaria.
Celebrating Women in Mathematics
The Fifth International Conference "Women in Mathematics in South-Eastern Europe" was officially opened, bringing together prominent mathematicians from a variety of fields. The event serves as a platform for fostering collaboration and highlighting the achievements of women in mathematics. The opening ceremony was graced by the presence of the President of the Bulgarian Academy of Sciences, Prof. Evelina Slavcheva. In her opening remarks, Prof. Slavcheva emphasized the essential role of women in advancing science, particularly in the field of mathematics.