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 [...]

Сбирка на семинара на МЦМН ще се проведе на 13.05.2025 г. (вторник) от 14:00 ч. в зала 403 на ИМИ - БАН. Докладчик: Milan Zlatanovic (University of Niš) Доклад: Non-symmetric gravitational theorys Резюме: We will consider a connection with totally skew-symmetric torsion on non-symmetric (semi-) Riemann manifolds that satisfy Einstein’s metric condition (EMC). We proved that an almost Hermitian manifold is a non-symmetric Riemann manifold that satisfies EMC if and only if it is a Nearly Kahler manifold. We will also show what happens in the case of para Hermitian manifold, contact, and para-contact manifolds that satisfy EMC. We show that a connection with skew symmetric torsion satisfying EMC exists on an almost contact metric manifolds when it is D-homothetic to a cosymplectic manifold. We [...]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 7 май 2025 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Binary Quadratic Forms and Conway’s Topographs (Lecture 2 of 3) ще изнесе Nikita Kalinin, Guangdong Technion Israel Institute of Technology. Следващата лекция ще бъде на 14.05.2025 от 16:00 ч. Abstract: Binary quadratic forms are as elementary as they are mysterious—much like prime numbers. In 1997, John Conway introduced topographs, a powerful geometric tool that provides a geometric visualization of binary quadratic forms and their values. These lectures will explore how topographs, combined with telescoping summation techniques, yield elegant formulas — some with intuitive geometric interpretations. For instance, consider the following result: Let A = \big\{ [...]

Съвместна сбирка на семинара на МЦМН и семинара "Алгебра и Логика" в ИМИ, София, ще се проведе идния вторник, с доклад на Георги Томанов, както следва. Вторник, 29-ти април, 14:00 часа, зала 403 на ИМИ-БАН. Георги Томанов, Université Claude Bernard, Lyon 1. Group action on homogeneous spaces and applications in number theory Abstract: Many longstanding conjectures and problems in number theory can be reformulated in terms of group actions on homogeneous spaces. This reformulation allows them to be tackled using, alongside deep methods from algebra and algebraic geometry, powerful tools from ergodic theory and dynamical systems. An example of the effectiveness of this approach is Margulis's groundbreaking proof of the Oppenheim conjecture (formulated in 1929) concerning the values of quadratic forms at integer points. In [...]

Следващата сбирка на Семинара по геометрия на МЦМН ще се проведе в сряда, 30 април 2025 г. от 16:00 ч. в зала 403 и онлайн в Zoom: Доклад на тема Binary Quadratic Forms and Conway’s Topographs (Lecture 1 of 3) ще изнесе Nikita Kalinin, Guangdong Technion Israel Institute of Technology. Следващите две лекции ще бъдат на 07.05.2025 и 14.05.2025 от 16:00 ч. Abstract: Binary quadratic forms are as elementary as they are mysterious—much like prime numbers. In 1997, John Conway introduced topographs, a powerful geometric tool that provides a geometric visualization of binary quadratic forms and their values. These lectures will explore how topographs, combined with telescoping summation techniques, yield elegant formulas — some with intuitive geometric interpretations. For instance, consider the following result: Let [...]

Дата: 11.04.2025 г., 16:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Felipe Espreafico Guelerman, Sorbonne Université - Paris Доклад: On Motivic and Arithmetic Donaldson-Thomas invariants Допълнителна информация: https://icms.bg/category/icms-seminar/ Резюме. Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic, A1-version of Donaldson-Thomas invariants from the motivic refinements first introduced in Kontsevich-Soibelman. Following ideas from Behrend, Bryan and Szendroi, we provide predictions for these invariants in a few simple examples, mainly the computation of DT invariants of A3. Our main goal is to draw relationships with the literature, including works of Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas among others. We begin with a brief introduction to A1-enumerative geometry and [...]