Следващото заседание на семинара на МЦМН ще се състои във вторник, 2 декември 2025 г. Доклади ще изнесат Рой Маген от МЦМН и Ливиу Орнеа от Букурещския университет, като вторият доклад е в рамките на съвместно заседание със семинара на секция "Анализ, Геометрия и Топология". Програмата е следната. ICMS Seminar and AGT Seminar Tuesday, December 2nd, room 403 IMI-BAS. 13:00 -- Roy Magen (ICMS, IMI-BAS)  Flavours of homotopy theory 14:00 -- Liviu Ornea (University of Bucarest)  Distinguished non-Kähler metrics on compact complex manifolds Abstract (Magen):    In this talk we will consider different flavours of homotopy theory for different types of geometric contexts. First we will recall the usual definitions of the homotopy category, and equivariant homotopy categories, and we will show how we can think of these in [...]

Семинар "Анализ, геометрия и топология" Вторник, 29 юли 2025 г., 13:00 ч., зала 403 на ИМИ - БАН. Speaker: Asia Mainenti, IMI and ICMS, Sofia Hodge-Riemann balanced structures on non-Kähler manifolds Резюме:  A Hodge-Riemann balanced structure on a complex manifold is the datum of a balanced metric whose (n-1)-th power can be decomposed into the wedge product of two differential forms, satisfying the classical Hodge-Riemann bilinear relations. Such structures were introduced by X. Chen and R. Wentworth, to generalize the nonabelian Hodge correspondence to non-Kähler Hermitian metrics. However, there are no known examples of Hodge-Riemann balanced structures on non-Kähler manifolds. The aim of this talk is to address this lack of examples, highlighting the relation with p-Kähler structures and discuss some obstruction results in [...]

Семинар "Анализ, геометрия и топология" Вторник, 22 юли 2025 г., 13:00 ч., зала 403 на ИМИ - БАН. Elia Fusi, University of Torino. Special metrics in hypercomplex geometry Резюме: The existence of special hyperHermitian metrics plays an important role in the study of hypercomplex manifolds. In this talk, after a brief overview of the basic definitions in hypercomplex Geometry, we will discuss two of the main types of special metrics in the hypercomplex setting: quaternionic Gauduchon and strong HKT metrics. First of all, we will discuss sufficient and equivalent conditions for a quaternionic Gauduchon metric to exist.  Afterwards, we will show that strong HKT and balanced hyperHermitian metrics cannot coexist on a compact non-hyperKähler manifold, proving a particular instance of the Fino-Vezzoni conjecture. Finally, [...]

Съвместна сбирка на семинара на МЦМН и семинара "Анализ, геометрия и топология" в ИМИ, София, ще се проведе идния вторник, с доклад на Elia Fusi, както следва. Вторник, 22-ри юли, 13:00 часа, зала 403 на ИМИ-БАН. Elia Fusi, University of Torino: Special metrics in hypercomplex geometry Abstract:The existence of special hyperHermitian metrics plays an important role in the study of hypercomplex manifolds. In this talk, after a brief overview of the basic definitions in hypercomplex Geometry, we will discuss two of the main types of special metrics in the hypercomplex setting: quaternionic Gauduchon and strong HKT metrics. First of all, we will discuss sufficient and equivalent conditions for a quaternionic Gauduchon metric to exist.  Afterwards, we will show that strong HKT and balanced hyperHermitian metrics [...]

На 15 юли 2025 г. от 13:00 часа в зала 403 на ИМИ-БАН ще се проведе съвместно заседание на Общия семинар на секция "Анализ, геометрия и топология" и Международния център по математически науки (ICMS-Sofia). Доклад на тема: Weak Metric Structures on Generalized Riemannian Manifolds ще изнесе Milan Zlatanovic, University of Niš, Serbia. Резюме. Linear connections with torsion are important in the study of generalized Riemannian manifolds (M , G=g+F ), where the symmetric part g of G is a non-degenerate (0,2)-tensor and F is the skew-symmetric part. Some space-time models in theoretical physics are based on (M, G=g+F) , where F is defined using a complex structure. In the lecture, we will show more general models, where F has constant rank [...]

Встъпителната лекция на доцент Михаил Школников в секция Анализ, геометрия и топология на ИМИ-БАН ще се проведе на 13.05.2025 г. (вторник) от 15:15 ч. в зала 403 на ИМИ - БАН. Докладчик: Михаил Школников (ИМИ - БАН) Доклад: Introduction to amoebas and tropicalization Резюме: We will start by reviewing the most classical aspects of the theory of amoebas deeply rooted in complex analysis and geometry. Next, we will pass to the notion of a tropical limit of amoebas, and will see how restoring the phase allows to recover topology and deduce intersection-theoretic results. After that, we will discuss some results (and their limitations) obtained with Grigory Mikhalkin in the context of non-commutative versions of amoebas of surfaces and tropical limits of curves inside the special matrix [...]

Поредното заседание на Общия семинар на секция "Анализ, геометрия и топология" ще се проведе на 22 октомври 2024 г. от 14:00 часа в зала 478 на ИМИ - БАН. Доклад на тема: Higher order estimates for Monge-Ampere type equations motivated by quaternionic geometry ще изнесе Marcin Sroka, Jagiellonian University, Kraków, Poland. Поканват се всички интересуващи се. Резюме. In the talk I will discuss obstacles for obtaining higher order a priori estimates for equation introduced by Alesker and Verbitsky in 2010 on HKT manifolds in relation to Calabi type conjecture on those manifolds (and similar type PDEs studied since on hypercomplex manifolds). After presenting the state of art, I will focus on the key second order estimate. For the real Monge-Ampere equation on Riemannian manifolds [...]

Поредното заседание на Общия семинар на секция "Анализ, геометрия и топология" ще се проведе на 15 октомври 2024 г. от 14:00 часа в зала 478 на ИМИ - БАН. Доклад на тема: Unimodality Preservation by Ratios of Functional Series and Integral Transforms ще изнесе Dmitrii Karp, Holon Institute of Technology, Holon, Israel. Поканват се всички интересуващи се. Резюме. Elementary, but very useful lemma due to Biernacki and Krzyz (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their corresponding coefficients. Over the last two decades it has been realized that, under some additional assumptions, similar claims hold for more general series ratios and integral transforms as well as for unimodality in place of monotonicity. [...]

Поредното заседание на Общия семинар на секция "Анализ, геометрия и топология" ще се проведе на 23 януари 2024 г. от 14:00 часа в зала 478 на ИМИ - БАН. Доклад на тема: Complex Dirac structures on flag manifolds ще изнесе Carlos Augusto Bassani Varea, Universidade Tecnológica Federal do Paraná, Brazil. Поканват се всички интересуващи се. Резюме. In this talk we present a description of the invariant complex Dirac structures with constant real index on a maximal flag manifold in terms of the roots of the Lie algebra which defines the flag manifold. As a particular case, when the real index is zero, we have the description of all invariant generalized complex structures on a maximal flag manifold. We also present a classification of the [...]

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. [...]