Mon, March 2, 2020
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5:00pm [5:15pm] Nitin Nitsure
Description:
Geometry and Topology seminar. Speaker: Nitin Nitsure. Date and Time: Monday 02 March, 05:15 pm - 06:30 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: Cotangent complex and applications -- Lecture No. 2. 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.

6:00pm