Общ семинар на секция "Анализ, геометрия и топология"
2024-10-15 14:00 - 15:30 (Europe/Sofia) | 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 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. In the talk, we discuss conditions on the functional sequence and the kernel of an integral transform ensuring such property. Numerous series and integral transforms appearing in applications satisfy our sufficient conditions, including Dirichlet, factorial and inverse factorial series, Laplace, Mellin and generalized Stieltjes transforms, among many others. The key role in our considerations is played by the notion of sign regularity.

Общ семинар на секция "Анализ, геометрия и топология"
2024-10-22 14:00 - 15:30
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 it follows essentially by Pogorelov calculation, for the complex Monge-Ampere equation, in relation to Calabi conjecture, it was proven by Aubin and Yau. I will use those two as comparison to underline new difficulties related to concavity properties of quaternionic Monge-Ampere operator.
Посещението на лектора е финансирано по Научна програма ” Повишаване на изследователския капацитет в областта на математическите науки (ПИКОМ)”, № ДО1-67/05.05.2022.

Встъпителна лекция на доц. Михаил Школников
2025-05-13 15:15 - 16:30
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 group SL(2,C). I will conclude by sketching a proof of the complete description of possible tropicalizations of families of analytic surfaces in SL(2,C) recently obtained with Peter Petrov, in particular, motivating our ongoing project on the non-commutative phase tropicalization, a few words about which will be said if time permits.

Общ семинар на секция "Анализ, геометрия и топология" и МЦМН
2025-07-15 13:00 - 14:30
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 and is based on weak metric structures (introduced by the V. Rovenski and R. Wolak), which generalize almost contact and (f)-contact structures. We consider metric connections (i.e., preserving (G)) with totally skew-symmetric torsion tensor. For (mbox{rank}(F)= mbox{dim} M) and non-conformal tensor (A^2), where (A) is a skew-symmetric (1,1)-tensor adjoint to (F), we apply weak almost Hermitian structures to fundamental results (by S. Ivanov and M. Zlatanovic) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kahler manifolds corresponding to eigen-distributions of (A^2). For (mbox{rank}(F)< mbox{dim} M) we apply weak (f)-structures and obtain splitting results for generalized Riemannian manifolds.
(This is joint work with Vladimir Rovenski, Department of Mathematics, University of Haifa).
Посещението на лектора е финансирано по Научна програма “Повишаване на изследователския капацитет в областта на математическите науки (ПИКОМ)”, № ДО1-67/05.05.2022.

Общ семинар на секция "Анализ, геометрия и топология" и МЦМН
2025-07-22 13:00 - 14:30
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 cannot coexist on a compact non-hyperKähler manifold, proving a particular instance of the Fino-Vezzoni conjecture. Finally, we will introduce an Einstein condition for hyperHermitian metrics and describe the similarities with the Kähler-Einstein case.
This is a joint work with Giovanni Gentili.

Повече информация можете да намерите на страницата на семинара:
https://icms.bg/category/icms-seminar/

Общ семинар на секция "Анализ, геометрия и топология"
2025-07-22 13:00 - 14:30
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, we will introduce an Einstein condition for hyperHermitian metrics and describe the similarities with the Kähler-Einstein case.
This is a joint work with Giovanni Gentili.

Общ семинар на секция "Анализ, геометрия и топология"
2025-07-29 13:00 - 14:30
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 the class of solvmanifolds. Lastly, we will present the first example of such a structure on a non-Kähler, non-compact complex manifold obtained as the product of the Iwasawa manifold by C. This is joint work with A. Fino.

Семинар на МЦМН и съвместно заседание със семинара АГТ
2025-12-02 13:00 - 16:00
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 terms of (equivariant) smooth manifolds. This will give us a suitable framework with which to adapt the notion of homotopy theory to different geometries.
We first use this framework to give a brief overview of the story in algebraic geometry, which produces motivic homotopy theory. Next, we will use our framework to discuss notions of homotopy theories parametrized by a geometric object, and discuss some consequences.
Depending on time constraints and interest, we will end either by discussing work relating this homotopical framework to 6-functor formalisms, by going over a version of this story in the complex analytic setting, or by introducing C∞-schemes and discussing possibilities for an extension of the story for manifolds to this setting.
Abstract (Ornea):

I shall review the definitions of LCK, pluriclosed and balanced metrics and discuss their incompatibility on the same compact complex manifold.

Съвместен семинар на МЦМН и секция АГТ
2026-06-02 13:00 - 14:30
Date and time: Tuesday, June 2-nd, 2026, 13:00, room 403 IMI-BAS
Lecturer: Bogdan Djordjevic, (Serbian Academy of Arts and Sciences, visitor at ICMS, IMI-BAS)
Title: Application of the Laplace transform for evaluating sums of hyperharmonic-like series in Banach algebras and modules
Abstract: In this talk it will be shown how the Laplace transform (in respective Banach spaces) can be utilized for evaluating sums of Banach-space-valued series. We demonstrate the technique on various abstract generalizations of the numerical hyperharmonic series, including noncommutative setting and non-invertible setting. As an application, we obtain new necessary consistency condition for the Sylvester equation ()ax-xb=c[latex].
