Thu, October 8, 2020
Public Access Category: All |
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- Time:
- 7:00pm
- Description:
- Title: Matrix orbit closures and their Hilbert functions.
Speaker: Alex Fink, Queen Mary University of London.
Time: 7pm IST (gate opens 6:45 pm IST).
Google Meet Link: meet.google.com/upg-tmyo-ekw.
Phone: (US) +1 929-266-1977 PIN: 832 926 004#.
Abstract: If an ordered point configuration in projective space is
represented
by a matrix of coordinates, the resulting matrix is determined up to
the action of the general linear group on one side and the torus of
diagonal matrices on the other. We study orbits of matrices under the
action of the product of these groups. The main question is what
properties of closures of these orbits, or quotients in other ambient
spaces, are determined by the matroid of the point configuration. The
main result is that the finely-graded Hilbert function is so
determined in characteristic 0 (we think also in general).
The results of mine in this talk are mostly joint with Andy Berget.