ncku-talk2022-11-10

Colloquium

DATE 2022-11-10　16:10-17:00

PLACE 數學系館 1F3174教室

SPEAKER Dr. Khan, Adeel Ahmad（中央研究院數學研究所）

TITLE Homological Resolutions of Singularities

ABSTRACT We will give a brief introduction to derived geometry with a view towards the study of singular spaces and algebraic varieties. In the derived world, every space admits a "resolution" by nonsingular (smooth) spaces, which we can regard as a homological version of a resolution of singularities. Just like derived functors in homological algebra, one can then use these resolutions to define derived versions of certain constructions such as tangent bundles, blow-ups, fundamental classes, and more.

Colloquium

DATE	2022-11-10　16:10-17:00

PLACE	數學系館 1F3174教室

SPEAKER	Dr. Khan, Adeel Ahmad（中央研究院數學研究所）

TITLE	Homological Resolutions of Singularities

ABSTRACT	We will give a brief introduction to derived geometry with a view towards the study of singular spaces and algebraic varieties. In the derived world, every space admits a "resolution" by nonsingular (smooth) spaces, which we can regard as a homological version of a resolution of singularities. Just like derived functors in homological algebra, one can then use these resolutions to define derived versions of certain constructions such as tangent bundles, blow-ups, fundamental classes, and more.