The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 27, 2020  at 2:00 p.m. in room 478 of IMI. A talk on: Characterizing surface by invariants will be delivered by Ognian Kassabov. Everybody is invited. Abstract. We will discuss the problem of characterizing geometric objects in the space by their invariants. For minimal surfaces the problem was solved in the works of Ganchev. On the other hand, Ganchev and Mihova considered the question in some more general cases. We propose a solution in the general case, and we characterize a surface by two invariant functions, subject of a differential equation.

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 16, 2020  at 1:00 p.m. in room 478 of IMI. A talk on: Functions Holomorphic over Algebras & Homological Mirror Symmetry will be delivered by Marin Genov. Everybody is invited. Abstract. We consider a generalization of the complex analysis of a single variable to finite-dimensional commutative associative algebras in place of C towards construction of smooth analytic curves over such algebras and possible applications to Homological Mirror Symmetry.

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on December 17, 2019  at 2:00 p.m. in room 478 of IMI. A talk on: Algebraic theory for continuity for meromorphic functions will be delivered by Antoni Rangachev, University of Chicago, IMI-BAS. Everybody is invited. Abstract. For a reduced complex analytic variety X and a rational number α between 0 and 1 I will show that the meromorphic functions on X that are Holder continuous with exponent α form a coherent sheaf that sits between the structure sheaf of X and its normalization. In fact, there are finitely many α that matter. For exponent α = 1 the result recovers the Lipschitz saturation considered by Pham-Teissier and Zariski. The [...]

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 26, 2019  at 1:00 p.m. in room 478 of IMI. A talk on: Topological Data Analysis (TDA) will be delivered by Peter Petrov, Institute of Mathematics and Informatics. Everybody is invited. Abstract. This talk is an introduction to TDA with an emphasis on persistent homology. It should be understandable for mathematicians as well as biologists, stressing geometric and intuitive explanations rather than formal arguments. Particular examples will be discussed.  

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on July 10, 2019 (Wednesday) at 2:00 p.m. in the Conference Room No. 256 of IMI. A talk on: Convolutional method in operational calculus will be delivered by Ivan Dimovski, Coresponding Member of BAS. Everybody is invited. Abstract. This lecture is intended as a kind of replica of the public defense of his thesis presented for Dr. Sc. degree in Mathematics, on occasion of the 85-th anniversary of Prof. Ivan Hristov Dimovski.  

A joint meeting of the Seminar of Analysis, Geometry and Topology Department and the Algebra and Logic Seminar will be held on April 09, 2019 at 14:00 in Room 478 of IMI. A talk on: Graded algebras, algebraic functions, planar trees, and elliptic integrals will be delivered by Vesselin Drensky, IMI-BAS. Everybody is invited. Abstract. The starting point of the talk is the problem how to measure how big an infinite dimensional algebra is. It has turned out that this problem concerns not only algebra. It is related with interesting problems in graph theory (enumeration of graphs with prescribed properties), mathematical analysis (e.g. theory of algebraic and transcendent functions). Even elliptic integrals surprisingly appear.

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on February 19, 2019 at 14:00 in Room 478 of IMI. A talk on: Cut-and-paste problem for polyhedral and algebraic varieties will be delivered by Peter Petrov, IMI-BAS. Everybody is invited. Abstract. The first part of this talk includes the history of Hilbert’s third problem, and the idea of the proof, proposed by Dehn, plus some more recent results. After formulating the problem for varieties and some related to it problems, we will review the main results obtained, and will discuss briefly the case of toric varieties.  

The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on November 6, 2018 at 14:00 in Room 478 of IMI. A talk on: Generalized Geometry in the Sense of Hitchin and Generalized Twistor Spaces will be delivered by Johann Davidov, IMI-BAS. Everybody is invited. Abstract. The concept of generalized complex geometry has been introduced by Nigel Hitchin and developed further by his students M. Gualtieri, G. Ca-valcanti, F. Witt as well as by many other mathematicians and physicists (including Hitchin himself). It generalizes both the concept of a complex structure and that of a symplectic one and can be considered as a complex analog of the notion of a Dirac structure introduced by T. Courant and A. [...]