||Stephen Doty (Loyola)
||Integral 2nd Fundamental Theorem of Invariant Theory for Partition Algebras|
|4||No talk, Spring break|
|| Emily Peters
||Categorifications: of the Jones polynomial and Temperley-Lieb|
|| Sarah Bockting-Conrad
|| Iva Halacheva (Northeasteern)
|| Allan Berele
||Double Centralizer Theorems, Invariant Theory and Trace Identities.|
|| Anne Dranowski (Toronto) ***time will likely be 2:45***
|| Tony Giaquinto
IES (the institute for environmental sustainability) is located at the corner of W. Sheridan and N. Kenmore Avenues, Chicago, IL (map)
Parking is available on-campus for $7 in the Parking Garage (building P1 on the Lake shore campus map). To get to the Parking Garage, enter campus at the corner of West Sheridan Road and North Kenmore Avenue.
February 26: Stephen Doty. Integral 2nd Fundamental Theorem of Invariant Theory for Partition Algebras
(Joint work with Chris Bowman and Stuart Martin.) There is a Schur-Weyl duality for a tensor power of a vector space, regarded as a bimodule for a symmetric group and partition algebra. We prove that the kernel of the action of the group algebra of the symmetric group is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra. The results are valid over an arbitrary integral domain. In consequence, the centralizer algebras of the partition algebra are cellular, and we provide an explicit cellular basis. We also prove similar results for the "half" partition algebras.
March 11: Emily Peters. Categorifications: of the Jones polynomial and Temperley-Lieb
This is an expository talk about categorification, specifically in the context of the Jones polynomial (Khovanov homology) and Temperley-Lieb (Brundan and Stroppel's approach via Khovanov arc algebras). Despite the preponderance of categories, there will be little-to-no abstract nonsense in this talk.
April 1: Allan Berele. Double Centralizer Theorems, Invariant Theory and Trace Identities.
In 1976 Procesi not only used the double centralizer theorem to prove the fundamental theorem of invariant theory of the general linear group, but he applied it to generic matrices and to trace identities. We also hope to talk about a number of more modern analogues including invariants of the general linear Lie superalgebra, wreath products and Sergeev algebras.