Time: February 6, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Vladimir Mitankin, IMI - BAS Title: A categorical view of singularity theory I Further information: https://icms.bg/a-categorical-view-of-singularity-theory-i-and-ii-talks-by-paul-horja/ Abstract. The mirror symmetry phenomenon was discovered by string theorists more than thirty years ago as an equivalence of two physical theories associated with very different geometries. The categorical point of view on this remarkable conjecture was famously introduced by M. Kontsevich in his 1994 ICM talk. As it became clear over time, homological mirror symmetry provides new approaches to many topics in symplectic and algebraic geometry. In these two talks, I will present a brief overview of the conjecture as well as some results inspired by mirror symmetry and obtained in joint work with [...]

Time: December 5, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Bogdan Stankov, IMI-BAS Title: Recent developments in the study of Følner functions For more information: https://icms.bg/recent-developments-in-the-study-of-folner-functions-talk-by-bogdan-stankov/  

Time: October 17, 2023, 2:00 pm Place: Room 403, IMI - BAS Speaker: Mikhail Shkolnikov, IMI-BAS Title: Tropical structures in sandpile model Abstract: The sandpile model is a cellular automaton that can be defined on any graph. Though it has appeared independently in a variety of contexts, it attracted tremendous attention from the wide scientific community when its instance on a large domain of the square lattice was put forward as the simplest rigorous example of self-organized criticality. Such phenomena, real-life examples of which are earthquakes, solar flares, or neuronal avalanches, could be vaguely described as being between order and chaos, demonstrating power laws without being finely tuned, and transcending the scale. Tropical geometry, on the other hand, is a field of pure mathematics [...]

The first meeting of the ICMS Seminar for 2023/2024 will be held on October 10, 2023, at 2:00 pm in Room 403 of IMI - BAS. A talk on: About a generalisation of Sylvester’s law of inertia will be delivered by Stéphanie Cupit-Foutou (Ruhr Universitat, Bohum). https://icms.bg/about-a-generalisation-of-sylvesters-law-of-inertia-talk-by-stephanie-cupit-foutou/ Abstract. Sylvester’s law of inertia can be formulated in terms of group actions when considering real linear groups acting on real quadratic forms by base change. After reviewing this celebrated result from this perspective, I will give a generalisation of it in the setting of so-called spherical varieties (a class of complex varieties including flag varieties, toric varieties, symmetric spaces, etc.). This is a joint work with D. Timashev