Time: March 27, 2025, 4:00 pm Place: Room 403, IMI - BAS Speaker: Luis Ugarte (University of Zaragoza, Spain) Title: Complex structures on Lie algebras and its application to the Hull-Strominger system Further information: https://icms.bg/category/icms-seminar/ Abstract. In this talk we will explain the role that the Lie algebras play in the construction of 6-dimensional compact quotient spaces M=G/Γ, where Γ is a lattice, endowed with an invariant complex structure with holomorphically trivial canonical bundle.We will use the approach of stable forms in six dimensions to provide a classification of unimodular Lie algebras admitting a complex structure with non-zero closed (3,0)-form. Some of these spaces can be equipped with balanced Hermitian metrics and they provide invariant solutions of the Hull-Strominger system, even with non-flat connection [...]

Time: March 25, 2025, 2:00 pm Place: Room 403, IMI - BAS Speaker: Mikhail Shkolnikov, IMI - BAS Title: Affine distance function Further information: https://icms.bg/category/icms-seminar/ Abstract. Affine geometry is sometimes described as "what remains of Euclidean geometry when distances are forgotten". In this talk, I will report on a very recent discovery of an affine-invariant notion, which may be viewed as a distance from a point inside a convex domain to its boundary. This new concept stems from a suggestion of Conan Leung, who proposed to average the canonical tropical series, a fundamental notion of tropical optics, over the manifold of all tropical structures of fixed covolume on the given affine space. Very little of what we (Nikita Kalinin, Ernesto Lupercio and me) currently [...]

Time: February 4, 2025, 2:00 pm Place: Room 403, IMI - BAS Speaker: Miroslav Georgiev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences Title: Yukawa regulators in electrodynamics: Exact approach to the self-energy and anomalous g-factor Further information: https://icms.bg/yukawa-regulators-in-electrodynamics-exact-approach-to-the-self-energy-and-anomalous-g-factor-icms-seminar-talk-by-miroslav-georgiev/ Abstract. 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. Highly accurate results for the electron’s and muon’s anomalous g-factor will be presented, with calculated values matching the most recent measurements reported in the [...]

Time: January 14, 2025, 2:00 pm Place: Room 403, IMI - BAS Speaker: Jean-Pierre Gazeau, Université Paris-Cité Title: Regularized Quantum Motion in a Bounded Set: Hilbertian Aspects Further information: https://icms.bg/regularized-quantum-motion-in-a-bounded-set-hilbertian-aspects-talk-by-jean-pierre-gazeau/ Abstract. It is well known that the momentum operator canonically conjugated to the position operator for a particle confined within a bounded interval of the line (with Dirichlet boundary conditions) is not essentially self-adjoint, as it possesses a continuum of self-adjoint extensions. 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. Reference: [...]

Time: September 10, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Boaz Moerman (Utrecht University) Title: Generalized integral points and strong approximation Further information: https://icms.bg/generalized-integral-points-and-strong-approximation-talk-by-boaz-moerman/ 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 \equiv a_i \mbox{ 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 \mathbb{Z} and the polynomials k[x] over a field k ). In this talk we will [...]