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 know, as well as necessary preliminaries, some observations and precise conjectures, will be covered during the talk, which mainly serves as an invitation to participate in developing this

The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences is organizing the international conference Diophantine and Rationality Problems (DRP2025). The conference will be held on March 10 – 14, 2025, in Sofia, Bulgaria.

The conference will explore the newest developments around classical qualitative and quantitative questions for rational, integral, Campana and related notions of points on schemes and stacks, together with new insights on rationality questions over non-closed fields.

Organisers: Ludmil Katzarkov, Vladimir Mitankin

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.

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.