Topology seminar
Speaker: Bittu Singh, IIT Bombay
Host: Rekha Santhanam
Title: Rational Homotopy theory
Time, day and date: 11:45:00 AM – 1:00:00 PM, Thursday, March 12
Venue: Room 215
Abstract: Dennis Sullivan introduced a framework in which the rational homotopy type of a topological space is encoded by commutative differential graded algebras (CDGAs). Earlier, Daniel Quillen established an equivalence between the rational homotopy category and an algebraic category, although this equivalence arises through a sequence of intermediate categorical constructions. In their paper “On PL De Rham Theory and Rational Homotopy Type”, A. K. Bousfield and Victor K. A. M. Guggenheim gave a precise formulation of Sullivan’s equivalence using the language of model category theory.
In this talk, we outline this approach and discuss the relationship between topological spaces and CDGAs in rational homotopy theory.

Commutative algebra seminar
Speaker: Prof. R. V. Gurjar
Host: Tony J P
Title: Singularities of plane curves III
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, March 12
Venue: Ramanujan Hall
Abstract: We will consider reduced power series f(X,Y) over an algebraically closed field k of characteristic 0. Following topics about R=k[[X,Y]]/(f) will be discussed. Algebraicity results of Artin, Hironaka-Rossi, Samuel, Basic intersection theory of place curves, Conductor ideal, Value semi-group of R, Gorenstein's result, Dedekind's Conductor Formula, Jung's formula connecting the Milnor number and conductor, Applications of Dedekind's formula. We will give Abhyankar's proofs of Dedekind and Gorenstein results. If time permits, Abhyankar-Moh result about generators of the value semi-group will be discussed.

Algebraic groups seminar
Speaker: Hariom Sharma, IIT Bombay
Host: Shripad Garge
Title: Subgroups of maximal rank
Time, day and date: 04:00:00 PM – 05:00:00 PM, Thursday, March 12
Venue: Room no. 215
Abstract: We continue with the third chapter of Digne Michel and study quasi-closed subsets of root systems.