Time: February 8, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Vladimir Mitankin, IMI - BAS Title: A categorical view of singularity theory II 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: January 30, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Vladimir Mitankin, IMI - BAS Title: Density of Hasse failures for diagonal affine cubic surfaces Further information: https://icms.bg/density-of-hasse-failures-for-diagonal-affine-cubic-surfaces-a-talk-by-vladimir-mitankin/ Abstract. А question of Mordell asks which integers are the sum of three cubes provided that there are no local obstructions to that. While Mordell’s question seems out of reach with the current machinery, it is widely believed that every integer not congruent to 4 or 5 mod 9 is a sum of three integral cubes. If, instead of the sum of three cubes, a general ternary cubic is considered, local conditions no longer suffice for solubility, i.e. the integral Hasse principle may fail. In this talk we shall apply the integral version of [...]

Time: January 16, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Carlos Varea (Universidade Tecnológica  Federal do Paraná - Campus Cornélio Procópio, Brazil) Title: The H-flux on flag manifolds generated by infinitesimal T-duality Further information: https://icms.bg/the-h-flux-on-flag-manifolds-generated-by-infinitesimal-t-duality-talk-by-carlos-varea/ Abstract. In this talk we present a new correspondence for pairs (\mathbb{F},H) formed by a flag manifold \mathbb{F} together with an $H$-flux on \mathbb{F} . Given its role within our correspondence, infinitesimal T -duality may be viewed as a source of H -flux, in the sense that it contributes towards taking fluxless pairs (\mathbb{F},0) to pairs (\mathbb{F}^\vee, H^\vee) carrying nontrivial flux H^\vee\neq 0 . We also illustrate how our correspondence exchanges complex structures with symplectic ones up to B -transformations. This is a [...]

Time: January 11, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Antoni Rangachev, IMI-BAS Title: The Milnor number of a smoothable curve Further information: https://icms.bg/the-milnor-number-of-a-smoothable-curve-talk-by-antony-rangachev/ Abstract. In this talk I will derive an algebraic formula for the Milnor number of a smoothable complex analytic curve singularity X by relating it to the Euler characteristic of its smoothing, which in turn I will relate to the multiplicity of the Jacobian ideal of X and and the multiplicity of X at its singular point. If time permits I will discuss generalizations to higher dimensions. This is a report on a joint work with Gaffney and Bengus-Lasnier.  

Time: January 9, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Antoni Rangachev, IMI-BAS Title: Stratified Morse theory and the critical locus of a linear functional Further information: https://icms.bg/stratified-morse-theory-and-the-critical-locus-of-a-linear-functional-talk-by-antony-rangachev/ Abstract. In this talk I will use stratified Morse theory to relate the number of critical points of a generic linear functional on a complex analytic manifold M to the Euler characteristics of M and a generic hyperplane slice of M.