Вітаємо всіх друзів Студматсемінару!

📢 Цього тижня ми рекомендуємо відвідати математичний семінар KSE.

А саме, цієї середи в KSE відбудеться виступ одного з найвідоміших українських алгебраїстів - Юрія Дрозда.

🔷 Тема: "König’s towers, quasi-hereditary chains and categorical resolutions".

👤 Спікер: Yuriy Drozd (Institute of Mathematics of NAS of Ukraine).

📅 Коли: 18 березня о 16:30-17:30.

📍 Де: KSE, Dragon Capital Building (вул. М. Шпака, 3), ауд. 4.07.

Abstract of the talk:

It is well-known that the classical resolution of singularities, even for curves, has some disagreeable features when one considers its effects on sheaves and especially on derived categories. Kuznetsov has proposed the notion of categorical resolution which should repair the situation. Analogous question is of importance in the theory of rings, algebras and modules, as M. Auslander noted.

We consider an approach to categorical resolution of singularities of rings and schemes (including non-commutative) based on the notion of minors and recollements (or bilocalizations). It provides a categorical resolution together with its semi-orthogonal decomposition. The latter gives estimates for the Rouquier dimension of the resolution and, hence, to that of the original derived category.

This approach gives an immediate result in 1-dimensional case, as well as for several special rings (Bäckström rings, gentle algebras, nodal orders and curves). Moreover, it often allows to describe the structure of the corresponding derived categories and/or establish its tilting to finite dimensional algbras.