Description
Geometry and Topology seminar.
Speaker: Nitin Nitsure.
Date and Time: Monday 24 February, 03:30 pm - 05:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Cotangent complex and applications (A short series of lectures).
Abstract: Differential 1-forms are very useful in the study of
multivariate calculus or smooth manifolds. Algebraically, the module of
Kahler differentials is very useful in commutative algebra. When the
spaces (or varieties) are not smooth but have singularities, differential
1-forms are not enough. Instead there is available a more general gadget
called the cotangent complex in commutative algebra as well as in
algebraic geometry. This series of talks will begin by recalling usual
differential forms and Kahler differentials in familiar setting, and then
introduce the cotangent complex. Applications to smoothness, local
complete intersections and deformation theory will be shown. Some
familiarity with the language of commutative algebra will be assumed.
The first talk will be accessible to advanced undergraduate students.