Institute of Mathematics and Informatics

Семинар "Дидактическо моделиране"
2023-10-09 14:30 - 16:00 (Europe/Sofia) | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредната сбирка на семинара
Дидактическо моделиране
ще се проведе на 09.10.2023 г. от 14:30 ч. в зала 278 на ИМИ.
Доклад на тема
Моделиране в задачи от две възстановени състезания
ще изнесат
Боянка Савова и доц. Ивайло Кортезов.

Семинар на МЦМН
2023-10-10 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 10.10.2023 г. (вторник) от 14:00 часа в зала 403 на ИМИ
ще се състои първата сбирка на семинара на МЦМН за 2023/2024 г.
Доклад на тема:
About a generalisation of Sylvester’s law of inertia
ще изнесе Stéphanie Cupit-Foutou (Ruhr Universitat, Bohum).
https://icms.bg/about-a-generalisation-of-sylvesters-law-of-inertia-talk-by-stephanie-cupit-foutou/
Резюме. Sylvester’s law of inertia can be formulated in terms of group actions when considering real linear groups acting on real quadratic forms by base change. After reviewing this celebrated result from this perspective, I will give a generalisation of it in the setting of so-called spherical varieties (a class of complex varieties including flag varieties, toric varieties, symmetric spaces, etc.). This is a joint work with D. Timashev

Семинар "Алгебра и логика"
2023-10-13 13:00 - 14:30 | Zoom
На 13 октомври 2023 г. (петък) от 13:00 часа ще се проведе хибридно (присъствено в зала 578 на ИМИ-БАН и онлайн чрез платформата zoom) заседание на семинара по „Алгебра и логика”.
Доклад на тема:
Emmy Noether’s Theorem on the Finite Generation of the Algebra of Invariants
ще изнесе Марин Генов (ИМИ – БАН).
Абстракт. I will introduce Emmy Noether’s theorem on the finite generation of invariants and give two proofs of it. As an example, I will also calculate the algebra of invariants of the dihedral group of order 2n acting on C[x,y].

Линк към Zoom-стаята на семинара:
https://us02web.zoom.us/j/85137375021?pwd=[REDACTED]

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================

Семинар на МЦМН
2023-10-17 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 17.10.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Михаил Школников, ИМИ – БАН
Доклад: Tropical structures in sandpile model
Резюме: The sandpile model is a cellular automaton that can be defined on any graph. Though it has appeared independently in a variety of contexts, it attracted tremendous attention from the wide scientific community when its instance on a large domain of the square lattice was put forward as the simplest rigorous example of self-organized criticality. Such phenomena, real-life examples of which are earthquakes, solar flares, or neuronal avalanches, could be vaguely described as being between order and chaos, demonstrating power laws without being finely tuned, and transcending the scale. Tropical geometry, on the other hand, is a field of pure mathematics often presented as a combinatorial version of algebraic geometry. I will tell how tropical curves arise in the scaling limit of the sandpile model in the vicinity of the maximal stable state and explain two major consequences inspired by this fact. The first one is that there is a continuous model for self-organized criticality, the only known model of a kind, defined in the realm of tropical geometry. The second is that the totality of recurrent states in the original sandpile model, the sandpile group, approximates a continuous group, a tropical Abelian variety, which is functorial with respect to inclusions of domains, allowing to compute its scaling limit as a space of circle-valued harmonic functions on the whole lattice.

Tropical structures in sandpile model, talk by Mikhail Shkolnikov, IMI-BAS

Семинар на секция "Изследване на операциите, вероятности и статистика"
2023-10-17 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 17 октомври 2023 (вторник) от 14:00 в зала 503 на ИМИ ще се проведе поредното заседание на семинара на секция „Изследване на операциите, вероятности и статистика”.
Доклад на тема:
On an Infinite-Time Horizon Linear-Quadratic Game with Constrained Control
ще изнесе Боян Стефанов.

Абстракт. A linear-quadratic game on an infinite horizon for continuous and discrete-time systems is studied when the controls of the minimizing player are constrained. Our approach is based on the approximation of this game by a suitable finite-time horizon game. First, the existence of a saddle point equilibrium is proved for the unconstrained case. Next, it is established that there exists a delta-neighborhood of the origin in the state space where the control constraints are not active. Using this neighborhood, the original problem is reduced to a suitable finite-time horizon game. The main result is a sufficient condition for the existence of saddle point equilibrium. As an illustration, the approach is applied to a basic monetary policy model. The discrete case is also briefly discussed.

Семинар "Алгебра и логика"
2023-10-20 13:00 - 14:30 | Zoom
На 20 октомври 2023 г. (петък) от 13:00 часа ще се проведе хибридно (присъствено в зала 578 на ИМИ-БАН и онлайн чрез платформата zoom) заседание на семинара по „Алгебра и логика”.
Доклад на тема:
Prime numbers and random walks in a square grid
ще изнесе Alberto Fraile (Czech Technical University in Prague, Czech Republic).
Съвместна работа с Osame Kinouchi, Prashant Dwivedi, Roberto Martínez, Theophanes E. Raptis и Daniel Fernández
Абстракт. One can argue that prime numbers present perplexing features, in a hybrid of local unpredictability and global regular behavior. It is this interplay between randomness and regularity that motivated searches for both local and global patterns that could potentially become signatures for certain underlying fundamental mathematical properties.In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk (PW). The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure – both in 2d and 3d – created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail [1].
[1] A. Fraile, O. Kinouchi, P. Dwivedi, R. Martínez, T. E. Raptis, D. Fernández, Prime numbers and random walks in a square grid, Phys. Rev. E 104 (5), 054114-054120 (2021).

Линк към Zoom-стаята на семинара:
https://us02web.zoom.us/j/85137375021?pwd=[REDACTED]

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================

Семинар "Дидактическо моделиране"
2023-10-23 14:30 - 16:00 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредната сбирка на семинара
Дидактическо моделиране
ще се проведе на 23.10.2023 г. от 14:30 ч. в зала 278 на ИМИ.
Доклад на тема
Върху модели от математически лагери и програми за ученици с изследователска цел в Европа
ще изнесe
Мирослав Маринов.

Семинар по Приложна математика
2023-10-25 15:00 - 16:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Крайни автомати и невронни мрежи за езиково моделиране
Докладчик: проф. Стоян Михов
Дата: 25.10.2023 г.
Час: 15:00 ч.
Място: Зала 503 на ИМИ-БАН
Резюме: Езиковите модели са основен инструмент за решаването на редица сложни задачи като извличане на информация, генерация на естествен език, машинен превод, речева комуникация и много други. Традиционно езиковите модели се представят с крайни преобразуватели. През последните години обаче езиковите модели, базирани на невронни мрежи, извършиха значителен скок в качеството на езиковото моделиране, с което се постигнаха близки до човешки способности в много задачи за разбиране на естествен език.
В предстоящата лекция ще направим първо кратък преглед на традиционните представяния на езикови модели, базирани на крайни преобразуватели. След това ще покажем често използвани архитектури на невронни мрежи за езиково моделиране и ще обсъдим техните предимства спрямо моделите, базирани на крайни преобразуватели.
В третата част на лекцията ще представим нашия подход за конструиране на ансамбли от крайни автомати, използвайки методите на дълбокото машинно обучение. По този начин ще комбинираме високото качество на невронните езикови модели с изчислителната ефективност на крайните автомати. Ще покажем, че клас от архитектури на невронни мрежи е изчислително изоморфен на клас от ансамбли от крайни автомати.
В заключение, ще представим емпирични резултати, показващи, че с помощта на нашия подход достигаме до перплексия (качество) на езиковите модели, реализирани с ансамбли от крайни автомати, конкурентна с перплексията на невронните езикови модели.
Фейсбук страница на семинара: Семинар по Приложна математика

Семинар на МЦМН
2023-10-30 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 30.10.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Петър Далаков, ИМИ – БАН
Курс: Introduction to Projective Structures and Opers
Резюме: A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

Introduction to Projective Structures and Opers, course by Peter Dalakov

Семинар на МЦМН
2023-10-31 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 31.10.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Петър Далаков, ИМИ – БАН
Курс: Introduction to Projective Structures and Opers
Резюме: A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

Introduction to Projective Structures and Opers, course by Peter Dalakov

Семинар на секция "Математически основи на информатиката"
2023-10-31 16:00 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 31 октомври 2023 г. (вторник) от 16:00 часа в зала 578 на ИМИ-БАН
ще се проведе заседание на семинара на секция
„Математически основи на информатиката”.
Доклад ще изнесе д-р Константин Воробьов (ИМИ – БАН).
Абстракт. In this work, we consider the problem of determining the exact value of (A_2(n, {d, d+2})) defined as the maximal cardinality of a binary code of length (n) with two possible distances (d) and (d+2). We prove that for fixed even (d) and (n) big enough, an optimal code must be a constant-weight code of weight (d/2+1) with possibly no more than one additional codeword of a different weight.
We also find exact values (A_2(n, {4, 6})) and (A_2(n, {6, 8})) starting from some (n).
This is a joint work with Ivan Landjev.

Семинар на МЦМН
2023-11-02 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 02.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Петър Далаков, ИМИ – БАН
Курс: Introduction to Projective Structures and Opers
Резюме: A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

Introduction to Projective Structures and Opers, course by Peter Dalakov

Семинар "Алгебра и логика"
2023-11-03 13:00 - 14:30 | Zoom
На 3 ноември 2023 г. (петък) от 13:00 часа ще се проведе дистанционно заседание на семинара по „Алгебра и логика”.
Доклад на тема:
A Reduction of Temporary Coalitions in Infinite Multiplayer Games
ще изнесе Димитър Гелев.
Абстракт. We propose a transformation of Concurrent Game Models which enables the reduction of infinite multiplayer games where players can form temporary coalitions to games with no coalitions by extending moves to include the negotiation steps that lead to the formation of coalitions. We adopt conditional promises as the building blocks of negotiation. Temporary coalitions and their agendas arise as the logical consequences of mutual promises. The transformation enables the use of established solution concepts about games with no coalitions for the analysis of games with temporary coalitions.

Линк към Zoom-стаята на семинара:
https://us02web.zoom.us/j/85137375021?pwd=[REDACTED]

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================

Семинар на МЦМН
2023-11-06 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 06.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Петър Далаков, ИМИ – БАН
Курс: Introduction to Projective Structures and Opers
Резюме: A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

Introduction to Projective Structures and Opers, course by Peter Dalakov

Общ семинар на секция "Анализ, геометрия и топология"
2023-11-07 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредното заседание на Общия семинар на секция “Анализ, геометрия и топология” ще се проведе
на 7 ноември 2023 г. от 14:00 часа в зала 478 на ИМИ – БАН.
Доклад на тема:
New and little known properties of the Fox and Fox-Wright functions
ще изнесе Dmitrii Karp, Holon Institute of Technology, Holon, Israel.
Поканват се всички интересуващи се.
Резюме. In the talk, I will introduce the functions H of Fox and W of Wright (its general case known as Fox-Wright function) and some motivation behind them. Then, I will discuss the extension of Gauss’ expansion and summation formulas for the hypergeometric function to the case of general Fox-Wright function and Norlund’s expansion for the Meijer’s G function to the case of Fox’s H function. I will further present positivity conditions for the so-called delta-neutral case of Fox’s H function making it a probability distribution (widely used in statistics), which rely on complete monotonicity of certain product ratios of Gamma functions. Moreover, I will exhibit a new integral equation for Fox’s H function and a conjecture regarding its zeros. Finally, some open problems will be presented.

Национален семинар по стохастика
2023-11-08 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредната сбирка на
Националния семинар по стохастика
ще се проведе на 8 ноември 2023 г. (сряда) от 14:00 часа в зала 503 на ИМИ – БАН.
Доклад на тема
Hamiltonicity of randomly perturbed graphs
ще изнесе
Alberto Espuny Díaz (Postdoctoral researcher at Universität Heidelberg, Germany).
Абстракт: In parallel to the development of smoothed analysis of algorithms, the study of randomly perturbed graphs has thrived in the combinatorics community. The setup is the following: one considers a dense graph $H$ which fails to satisfy some increasing property and then sprinkles edges randomly until the property appears. A main goal in the area is to understand how many random edges are needed, and which graphs $H$ are “worst” for this problem.
In this talk I will survey some results in the area and focus particularly on the Hamiltonicity problem, which has often been used as a test for many techniques in graph theory. I will present several variants of the problem, as well as some results for each of these variants. The talk is based on joint works with Alexander Allin, António Girão, and Joseph Hyde.

Национален семинар по стохастика
2023-11-08 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредната сбирка на
Националния семинар по стохастика
ще се проведе на 15 ноември 2023 г. (сряда) от 14:00 часа в зала 503 на ИМИ – БАН.
Доклад на тема
Anti-concentration of Rademacher sums and Tomaszewski’s counterpart problem
ще изнесе
Julien Portier, University of Cambridge.
Абстракт

Семинар по геометрия на МЦМН
2023-11-08 16:00 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Следващото заседание на семинара по геометрия на МЦМН ще се проведе на
8 ноември 2023 г., сряда, от 16:00 ч. в зала 403 и онлайн. Доклад на тема
Tropicalizations II
ще изнесе Михаил Школников, ИМИ – БАН.
Абстракт: I will start by briefly recalling the two approaches to tropicalizing subvarieties of algebraic tori. We then transition to the compactified version, substituting the torus with a toric variety, and formalizing the concept of embedded tropical varieties together with a notion of their smoothness. Notably, not all such varieties can be realized as tropicalizations of classical varieties, and different embeddings of classical varieties yield combinatorially distinct tropicalizations, which we equate through so-called modifications. We will conclude by addressing the question of recovering information about classical varieties from their tropicalizations, exemplified by the phase tropical limit having the same topology as corresponding complex hypersurfaces provided that the usual tropicalization is smooth.

Tropicalizations II, a talk by M. Shkolnikov

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар "Алгебра и логика"
2023-11-10 13:00 - 14:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 10 ноември 2023 г. (петък) от 13:00 часа ще се проведе хибридно заседание (присъствено в зала 578 на ИМИ-БАН и онлайн чрез платформата zoom) на семинара по „Алгебра и логика”.
Доклад на тема:
Transfinite version of the Mittag-Leffler condition for the vanishing of the derived limit
ще изнесе
Mishel Carelli (Technion – Israel Institute of Technology, Israel).
Абстракт. We give a necessary and sufficient condition for an inverse sequence S0 ← S1 ← . . . indexed by natural numbers to have lim¹S = 0. This condition can be treated as a transfinite version of the Mittag-Leffler condition. We consider inverse sequences in the category of abelian groups. We also show that the class of inverse sequences S such that lim S = lim¹S = 0 is the least class of inverse sequences containing the trivial inverse sequence and closed with respect to small limits and a certain type of extensions.
Линк към Zoom-стаята на семинара:
https://us02web.zoom.us/j/85137375021?pwd=[REDACTED]

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================

Семинар на секция "Математически основи на информатиката"
2023-11-10 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 10 ноември 2023 г. (вторник) от 14:00 часа в зала 478 на ИМИ-БАН
ще се проведе заседание на семинара на секция
„Математически основи на информатиката”.
Доклад на тема
On induced (C_4)-free graphs with high average degree
ще изнесе Антонио Жирао.
Абстракт. A long-standing conjecture of Thomassen from the 80’s states that every graph with sufficiently high average degree contains a subgraph with high girth and still preserving large enough average degree. This conjecture has only been resolved in the early 2000’s by Kühn and Osthus in the first non-trivial case i.e. they showed that for every (k), there is (f(k)) such the every graph with average degree at least (f(k)) contains a subgraph which is (C_4)-free with average degree (k).
We will talk about a recent result which strengthens this result of Kühn and Osthus in two ways. First, we prove an analogous induced version and secondly we give much better bounds for the function f allowing us obtain few non-trivial results as simple corollaries. Finally, we use these methods to confirm a conjecture Bonamy et al.
Антонио Жирао e пост-докторант в Оксфордския Университет под ръководството на проф. Алекс Скот. Преди да заеме тази позиция, Антонио работи като пост-докторант в Хайделбергския Университет под ръководството на проф. Феликс Йоос и в Университета в Бирмингам под ръководството на проф. Даниела Кюн и проф. Дерек Остюс. Защитава докторантурата в Университета в Кеймбридж под ръководството на проф. Бела Болобаш през 2018 г.

Семинар на МЦМН
2023-11-14 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 14.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Валдемар Цанов, ИМИ – БАН
Курс: Invariant theory, homogeneous projective varieties, and momentum maps
Резюме: Let (f:Kto U(V)) be a unitary representation of a compact Lie group (K) with Lie algebra (mathfrak k). This series of talks will be devoted to some recent developments based on relations between the following three classical notions.

The ring of -invariant polynomials (mathbb C[V]^K) is finitely generated by homogeneous elements, by a theorem of Hilbert, but the proof is notoriously nonconstructive. The degrees of a minimal set of generators are canonically determined by (f), and will be the focus of the discussion.
The (K)-equivariant momentum map (mu:mathbb P(V)to mathfrak k^*) associated to the Fubini-Study form encodes in its image properties of the invariant ring (mathbb C[V]^K) and the (K)-module structure of the entire polynomial ring (mathbb C[V]), due to theorems of Mumford and Brion. While many general properties of momentum images have been established, explicit descriptions remain unknown in many cases south for in physics and quantum information theory.
Projective geometry of complex (K)-orbits in (mathbb P(V)); their fundamental forms, osculating varieties and secant varieties.

General relations between the first two topics are well established, even in a more general context. There are also well known relations between invariant theory and projective geometry, but secant varieties have only recently been brought to the discussion and are subject of current interest.
After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov

Семинар по Приложна математика
2023-11-14 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
How log-concavity fought lottery frauds in Florida and what it did after winning
Докладчик: Дмитри Карп
Дата: 14.11.2023 г.
Час: 14:00 ч.
Място: Зала 503 на ИМИ-БАН
Резюме: In the talk I will first discuss the log-concavity in parameters of the normalized beta function (which represents the cumulative distribution function of beta distributed random variable) that has been used recently in an investigation of lottery frauds in Florida. I will then present some related properties of incomplete beta function and proceed to general log-concavity problems and their particular cases motivated by various problems in statistics, probability and analysis.
Фейсбук страница на семинара: Семинар по Приложна математика

Национален колоквиум по математика
2023-11-14 16:15 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
СЪЮЗ НА МАТЕМАТИЦИТЕ В БЪЛГАРИЯ

ИНСТИТУТ ПО МАТЕМАТИКА И ИНФОРМАТИКА – БАН

НАЦИОНАЛЕН КОЛОКВИУМ ПО МАТЕМАТИКА

​Поредната сбирка на Колоквиума ще се състои на 14 ноември 2023 г. (вторник) от 16:15 часа в Заседателната зала на ИМИ – БАН. Доклад на тема:

Arcs of High Divisibility and Their Applications to Coding Theory
ще изнесе проф. дмн Иван Ланджев,
Институт по матем​атика и информатика, Българска академия на науките.

​Резюме

Семинар по геометрия на МЦМН
2023-11-15 16:00 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 15 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:

Topics in non-archimedean analytic geometry (I),
by Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар на МЦМН
2023-11-16 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 16.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Валдемар Цанов, ИМИ – БАН
Курс: Invariant theory, homogeneous projective varieties, and momentum maps
Резюме: Let (f:Kto U(V)) be a unitary representation of a compact Lie group (K) with Lie algebra (mathfrak k). This series of talks will be devoted to some recent developments based on relations between the following three classical notions.

The ring of -invariant polynomials (mathbb C[V]^K) is finitely generated by homogeneous elements, by a theorem of Hilbert, but the proof is notoriously nonconstructive. The degrees of a minimal set of generators are canonically determined by (f), and will be the focus of the discussion.
The (K)-equivariant momentum map (mu:mathbb P(V)to mathfrak k^*) associated to the Fubini-Study form encodes in its image properties of the invariant ring (mathbb C[V]^K) and the (K)-module structure of the entire polynomial ring (mathbb C[V]), due to theorems of Mumford and Brion. While many general properties of momentum images have been established, explicit descriptions remain unknown in many cases south for in physics and quantum information theory.
Projective geometry of complex (K)-orbits in (mathbb P(V)); their fundamental forms, osculating varieties and secant varieties.

General relations between the first two topics are well established, even in a more general context. There are also well known relations between invariant theory and projective geometry, but secant varieties have only recently been brought to the discussion and are subject of current interest.
After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov

Семинар "Алгебра и логика"
2023-11-17 13:00 - 14:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
На 17 ноември 2023 г. (петък) от 13:00 часа ще се проведе хибридно заседание (присъствено в зала 578 на ИМИ-БАН и онлайн чрез платформата zoom) на семинара по „Алгебра и логика”.
Доклад на тема:
Noncommutative invariants of dihedral groups
ще изнесе
Боян Костадинов, ИМИ – БАН.
Абстракт. We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators of the algebra of invariants. In the Lie case, when the algebra of invariants is not finitely generated, we give a minimal system of generators of the invariants in the commutator ideal as a module of the algebra of the invariants in the polynomial algebra in two variables. In both associative and Lie cases we compute the Hilbert series of the algebras of invariants.
The results are obtained jointly with Vesselin Drensky.
Линк към Zoom-стаята на семинара:
https://us02web.zoom.us/j/85137375021?pwd=[REDACTED]

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================

Семинар "Дидактическо моделиране"
2023-11-20 14:30 - 16:00 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Поредната сбирка на семинара
Дидактическо моделиране
ще се проведе на 20.11.2023 г. от 14:30 ч. в зала 278 на ИМИ.
Доклад на тема
Точкуване на задачи и използване на скàли при стандартизирани оценявания
ще изнесe
проф. Кирил Банков.

Семинар на МЦМН
2023-11-21 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 21.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Валдемар Цанов, ИМИ – БАН
Курс: Invariant theory, homogeneous projective varieties, and momentum maps
Резюме: Let (f:Kto U(V)) be a unitary representation of a compact Lie group (K) with Lie algebra (mathfrak k). This series of talks will be devoted to some recent developments based on relations between the following three classical notions.

The ring of -invariant polynomials (mathbb C[V]^K) is finitely generated by homogeneous elements, by a theorem of Hilbert, but the proof is notoriously nonconstructive. The degrees of a minimal set of generators are canonically determined by (f), and will be the focus of the discussion.
The (K)-equivariant momentum map (mu:mathbb P(V)to mathfrak k^*) associated to the Fubini-Study form encodes in its image properties of the invariant ring (mathbb C[V]^K) and the (K)-module structure of the entire polynomial ring (mathbb C[V]), due to theorems of Mumford and Brion. While many general properties of momentum images have been established, explicit descriptions remain unknown in many cases south for in physics and quantum information theory.
Projective geometry of complex (K)-orbits in (mathbb P(V)); their fundamental forms, osculating varieties and secant varieties.

General relations between the first two topics are well established, even in a more general context. There are also well known relations between invariant theory and projective geometry, but secant varieties have only recently been brought to the discussion and are subject of current interest.
After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov

Семинар по геометрия на МЦМН
2023-11-22 16:00 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 22 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:

Topics in non-archimedean analytic geometry (II)

by Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар на МЦМН
2023-11-23 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Дата: 23.11.2023 г., 14:00 ч.
Място: Зала 403, ИМИ – БАН
Докладчик: Валдемар Цанов, ИМИ – БАН
Курс: Invariant theory, homogeneous projective varieties, and momentum maps
Резюме: Let (f:Kto U(V)) be a unitary representation of a compact Lie group (K) with Lie algebra (mathfrak k). This series of talks will be devoted to some recent developments based on relations between the following three classical notions.

The ring of -invariant polynomials (mathbb C[V]^K) is finitely generated by homogeneous elements, by a theorem of Hilbert, but the proof is notoriously nonconstructive. The degrees of a minimal set of generators are canonically determined by (f), and will be the focus of the discussion.
The (K)-equivariant momentum map (mu:mathbb P(V)to mathfrak k^*) associated to the Fubini-Study form encodes in its image properties of the invariant ring (mathbb C[V]^K) and the (K)-module structure of the entire polynomial ring (mathbb C[V]), due to theorems of Mumford and Brion. While many general properties of momentum images have been established, explicit descriptions remain unknown in many cases south for in physics and quantum information theory.
Projective geometry of complex (K)-orbits in (mathbb P(V)); their fundamental forms, osculating varieties and secant varieties.

General relations between the first two topics are well established, even in a more general context. There are also well known relations between invariant theory and projective geometry, but secant varieties have only recently been brought to the discussion and are subject of current interest.
After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov
