The study of codes over the rings (ring-linear codes) attracted great interest after the work of Calderbank, Hammons, Kumar, Sloane, and Sole in the early 1990s. In this seminar, the basic theory of linear codes over finite commutative rings will be presented including the importance of codes over rings, various kinds of rings for ring-linear coding theory, the weight functions on finite rings, MacWilliams equivalence theorem and the connection between these codes and codes over fields via the Gray maps. Moreover, the cyclic codes over finite commutative rings will be considered. Finally, some well-known generalizations of cyclic codes such as negacyclic, quasi-cyclic, polycyclic, multivariable, polynomial and Abelian codes will be introduced.
We investigate lattice packings of Minkowski balls and domains. By results of the proof of Minkowski conjecture about the critical determinant we divide the balls and domains on 3 classes: Minkowski, Davis and Chebyshev-Cohn. The optimal lattice packings of the balls and domains are obtained. The minimum areas of hexagons inscribed in the balls and domains and circumscribed around them are given. These results lead to algebro-geometric structures in the framework of Pontrjagin duality theory.
In recent months, several new results were obtained in Homological Mirror Symmetry. The purpose by now, in this traditional winter conference, is to survey these results and open new directions for development and collaboration.
Andrés Navas is a mathematician specializing in dynamical systems, geometry, and group theory and is a world-renowned expert in ergodic theory. He was a student of Étienne Ghys. For his scientific achievements, he was awarded the MCA prize.
In this introductory talk, I will present some concepts surrounding singularities and why and how we look for their resolutions.
I will talk about joint work with Shing-Tung Yau, Sergei Gukov, and earlier joint work with Gholampour and Yau on Mathematical definition of Vafa-Witten invariants on 4 and 3 dimensional manifolds.
In this series of talks, we will explore how the field of self-organized criticality is useful to inform the structure of artificial models of life. This is joint work with Kalinin, Tabares and Shkolnikov, and with Cruz, Muñoz and Viafara.
The International Center for Mathematical Sciences received a three-year grant from Simons Foundation
The good news was announced personally by Prof. Yuri Tschinkel, Director of Mathematics and Physical Sciences division of Simons Foundation, during his visit to Sofia. The Foundation funded a project of the International Center for Mathematical Sciences (ICMS-Sofia) at the Institute of Mathematics and Informatics for a period of three years. The funds will be used to organize international scientific forums with the participation of world-renowned and established mathematicians, to open new positions for researchers and to support scientists from Ukraine and other countries.
The goal of this conference to consolidate and disseminate new developments in Geometry and Physics. The list of participants includes: Maxim Kontsevich, Institut des Hautes Études Scientifiques, France, Phillip Griffiths, Institute for Advanced Study, Karim Adiprasito, University of Copenhagen, Denmark, Vivek Shende, Centre for Quantum Mathematics, Syddansk Universitet, Denmark, Jørgen Ellegaard Andersen, University of Southern Denmark, Denmark, Oscar García-Prada, Instituto de Ciencias Matemáticas (ICMAT), Spain, Kenji Fukaya, Simons Center for Geometry and Physics at Stony Brook, USA, Mina Teicher, Bar-Ilan University, Israel, Robert Stephen Cantrell, University of Miami, USA, Yong-Geon Oh, IBS Center for Geometry and Physics, Korea, Ernesto Lupercio, Cinvestav-IPN, México, Tony Pantev, University of Pennsylvania, USA, Ludmil Katzarkov, University of Miami, USA and Institute of Mathematics and Informatics, Bulgaria, Meral Tosun, Galatasaray University, Turkey.
This workshop will be devoted to discussing important and timely problems concerning the application of exact mathematical methods to conventional integrable systems and to the gauge/string models, e.g., to extend current methods for calculating finite-volume matrix elements of operators, to construct a finite version of the hexagon form factor expansion for short operators, to extend the methods of the thermodynamic Bethe Ansatz to world-sheets of higher topology and to all sorts of boundaries and defects, etc.