Configuration Spaces

Learning Seminar on Configuration Spaces & their Cohomology

January -- April 2015

The long-term goal of this learning seminar is to understand recent advances in representation stability; a recent idea developed by Benson Farb and Thomas Church. The current plan (till April) is to start with configuration spaces, their cohomology and then move on to the representation theoretic study done by Lehrer and Solomon.

Day : Every Friday (first lecture Jan 23)

Time : 11:50 - 12:40

Place : Lecture Hall 5.

Reference Material

Arnol'd V. I. The cohomology ring of the group of colored braids. Mat.Zametki (Math. Notes), 1969, 5:2, 227-231. pdf
Cohen F. Cohomology of braid spaces. Bulletin of the American Mathematical Society, 79(4):763–766, 1973. link
Farb, Benson, Representation Stability, to appear in the Proceedings of the 2014 Seoul ICM. pdf
Farb, B.; Church T.; Ellenberg J. FI-modules: a new approach to stability for S_n-representations, to appear in Duke Mathematical Journal. pdf
Farb, B.; Church T. Representation theory and homological stability, Advances in Math. , Vol. 245 (2013), 250-314. pdf
Lehrer, G. and Solomon, L. On the action of the symmetric group on the cohomology of the complement of its reﬂecting hyperplanes, J. Algebra
104 (1986), no. 2, 410–424. link

Lectures Schedule

No.	Date	Speaker	Topic
1	23/01/2015	Priyavrat	Introduction
2	30/01/2015	Ronno	Braid groups I
3	06/02/2015	Ronno	Braid groups II
4	13/02/2015	Priyavrat	Cohomology of hyperplane complements
5	20/02/2015		No seminar
6	27/02/2015		No talk, exam week
7	06/03/2015	Shraddha	Irreducible representations of the symmetric group I
8	13/03/2015	Shraddha	Irreducible representations of the symmetric group II
9	20/03/2015	Ronno	FI-modules I