Non UBC
DSpace
Saugata Basu
2019-11-24T10:55:06Z
2019-05-27T16:10
The cohomology groups (with rational coefficients) of semi-algebraic sets defined by symmetric polynomials inherit a structure of a finite dimensional module over the symmetric group (from the action of the symmetric group on the ambient space). The isotypic decomposition of these modules shed important information on the Betti numbers of such sets, via the multiplicities of the various irreducible representations (the so called Specht modules), and the well known ``hook formula'' that gives the dimensions of these irreducible representations. We prove new vanishing results on the multiplicities of these Specht modules in the cohomology groups of semi-algebraic sets defined by symmetric polynomials (in each dimension).
https://circle.library.ubc.ca/rest/handle/2429/72386?expand=metadata
35.0 minutes
video/mp4
Author affiliation: Purdue University
Banff (Alta.)
10.14288/1.0385850
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Operations Research, Mathematical Programming, Algebraic Geometry, Control/Optimization/Operation Research
Vandermonde varieties, mirrored spaces, and cohomology of symmetric semi-algebraic sets
Moving Image
http://hdl.handle.net/2429/72386