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 [...]

На 28 март 2025 г. (петък) от 13:00 часа в зала 578 на ИМИ и онлайн чрез Zoom ще се проведе хибридно заседание на семинара по „Алгебра и логика”. Доклад на тема: Graded algebras that are the sum of two homogeneous subalgebras ще изнесе Пламен Кошлуков (State University of Campinas, Brazil). Абстракт. Let A be an algebra over a field F, graded by a group G, and let B and C be two homogeneous subalgebras of A such that A=B+C. We study the following problem: If B and C satisfy graded identities, does the same also hold for A? The analogous problem for algebras without any grading was proposed in 1994 by Beidar and Mikhalev; in implicit form it appeared in a paper by O. Kegel, in 1963. Several particular cases were [...]

Дата: 27.03.2025 г., 16:00 ч. Място: Зала 403, ИМИ - БАН Докладчик: Luis Ugarte, University of Zaragoza, Spain Доклад: Complex structures on Lie algebras and its application to the Hull-Strominger system Допълнителна информация: https://icms.bg/category/icms-seminar/ Резюме. In this talk we will explain the role that the Lie algebras play in the construction of 6-dimensional compact quotient spaces M=G/Γ, where Γ is a lattice, endowed with an invariant complex structure with holomorphically trivial canonical bundle.We will use the approach of stable forms in six dimensions to provide a classification of unimodular Lie algebras admitting a complex structure with non-zero closed (3,0)-form. Some of these spaces can be equipped with balanced Hermitian metrics and they provide invariant solutions of the Hull-Strominger system, even with non-flat connection on [...]