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The talk aims to review the progress in the study of higher rank P-and Q-polynomial association schemes, starting with the foundational concepts and recent advancements as outlined in the referenced papers. It will provide explicit examples of multivariate P-and Q-polynomial association schemes and explore the implications of these developments. The discussion will draw from multiple sources, including recent significant contributions by Bernard et al. and Crampé et al., and will conclude with speculations on future directions for research in this area.

This talk is based on the two joint papers with Hirotake  Kurihara (Yamaguchi University), Da Zhao (East China University of Science  and Technology) and Yan Zhu (Shanghai University for Science and Technology).  

A seminar talk by Daniela Martinez Correa, Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”

A seminar talk by Morgan Brown, University of Miami.

I will present a form of quantum circuit complexity that extends to open systems. To illustrate the methodology, I  focus on a basic model where the Hilbert space of states is represented by the Euclidean plane. Specifically, the  investigation is about the dynamics of mixed quantum states as they undergo interactions with a sequence of gates.

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 L. Katzarkov about classical problems on discriminants and singularity theory.

A talk by Carlos Varea, (Universidade Tecnológica Federal do Paraná - Campus Cornélio Procópio, Brazil) on January 16, 14:00 Sofia time.

We study various correspondences between finite-dimensional nilpotent algebras and (quasi)groups similar to those given by the circle product in the case of associative algebras or by the Baker-Campbell-Hausdorff formulas in the case of Lie algebras or their generalizations. In the particular case of Malcev's correspondence, we obtain some new results about groups using Lie algebras and vice versa.

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.