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So far tbranzov has created 52 blog entries.
28 04, 2022

Coding Theory, Combinatorial Designs, and Finite Geometry

2022-05-09T12:32:42+03:00April 28th, 2022|Colloquium|

Error-correcting codes are used to protect data from random errors in satellite and wireless communication systems, audio and video recording devices, and data storage devices. A large class of codes with a wide range of applications are based on finite geometry. The most notable example of such codes are the Reed-Muller codes that are being used in deep space and mobile communications. The subject of this talk is a class of codes based on combinatorial designs. These combinatorial codes possess remarkable error-correction properties, admit efficient decoding, and present a viable alternative to a subclass of Reed-Muller codes.

18 04, 2022

Functional Inequalities and Improvements: Stability

2022-07-18T13:39:11+03:00April 18th, 2022|Consortium Distinguished Lecture Series|

Functional inequalities constitute a very useful toolbox in various fields of Mathematics, like analysis, spectral analysis, mathematical physical, theory of partial differential equations and differential geometry. For each of them, knowing the best constant in the inequality and as much as possible about the extremal, optimizing, functions is very important. In these presentations I will describe how this field has developed very strongly in the last decades and how now we dispose of a good set of strategies to address all the above issues for a large family of inequalities. Also a recent set of important results are devoted to the improved inequalities that can be written for non optimizers, topic which is denoted as “stability” for the inequalities. The methods that one can use and the different results that have been obtained will be discussed via the choice of a set of particular inequalities which enjoy interesting features or that are very useful in particular applications.

11 04, 2022

Introductory Toric Geometry

2022-07-18T13:47:04+03:00April 11th, 2022|ICMS Seminar|

This is the first part, consisting of four lectures, of a mini-course in which the combinatorial geometry related to toric varieties will be introduced. It will be developed to define and express properties of toric varieties and toric morphisms, and to investigate the geometry of the orbits by the torus action, in particular the orbit decomposition. Next, toric divisors, invertible and reflexive sheaves on toric variety, and their groups will be introduced and studied.

9 03, 2022

Higgs bundles on elliptic surfaces and logarithmic transformations, Kyoung-Seog Lee

2022-03-09T15:59:54+02:00March 9th, 2022|Joint ICMS & IMSA Seminar|

Logarithmic transformation is an important operation introduced by Kodaira in the 1960s. One can obtain an elliptic surface with multiple fibers by performing logarithmic transformations on an elliptic surface without multiple fibers. On the other hand, vector bundles on elliptic surfaces are important objects in many branches of mathematics, e.g., algebraic geometry, gauge theory, mathematical physics, etc. In this talk, I will discuss how certain Higgs bundles on elliptic surfaces are changed via logarithmic transformations. This talk is based on a joint work with Ludmil Katzarkov

17 02, 2022

Birational geometry of sextic double solids with a compound A_n singularity

2022-02-18T09:14:03+02:00February 17th, 2022|Joint ICMS & IMSA Seminar|

Sextic double solids, double covers of ℙ^3 branched along a sextic surface, are the lowest degree Gorenstein Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are ℚ-factorial with ordinary double points, are known to be birationally rigid. In this talk, we discuss birational geometry of sextic double solids with an isolated compound A_n singularity. I have shown that n is at most 8, and that rigidity fails for n > 3.

4 02, 2022

Windows and Geometric Invariant Theory

2022-02-04T13:05:05+02:00February 4th, 2022|Joint ICMS & IMSA Seminar|

The theory of windows was introduced relatively recently by both Halpern-Leistner and Ballard, Favero and Katzarkov, and is a great tool to study derived categories of algebraic varieties that appear as GIT constructions, as well as their behaviour at wall crossings as we vary the stability conditions.

2 02, 2022

Sampling with Minimal Energy: A talk in commemoration of Bl. Sendov’s 90th birth date.

2022-02-07T11:04:25+02:00February 2nd, 2022|Consortium Distinguished Lecture Series|

The International Center for Mathematical Sciences at the Institute of Mathematics and Informatics (ICMS–Sofia) will commemorate the 90th anniversary of the birth of Prof. Sendov with a special talk by Edward Saff from Vanderbilt University, USA - "Sampling with Minimal Energy: A talk in commemoration of Bl. Sendov's 90th birth date."

2 02, 2022

90th anniversary of the birth of Professor Blagovest Sendov

2022-07-18T13:30:18+03:00February 2nd, 2022|News|

February 8, 2022, marks the 90th anniversary of the birth of Blagovest Sendov. He passed away on January 19, 2020, shortly before reaching the age of 88. The Institute of Mathematics and Informatics and the ICMS will commemorate the 90th anniversary of the birth of Prof. Sendov with a talk by Edward Saff from Vanderbilt University, USA - "Sampling with Minimal Energy: A talk in commemoration of B. Sendov's 90th birth date."

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