February 28, 2022 - March 4, 2022
Public Access Category: All |
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- Time:
- 2:30pm-3:45pm
- Description:
- Reading Seminar
Thursday, 3rd March · 2:30 – 3:45 pm
Google Meet joining info
Video call link: https://meet.google.com/auv-mwkn-ixh
Title: Modular representations of Algebraic groups,
Abstract:
We have studied the Borel-Weil-Bott theorem and Kempf vanishing theorem. Using Serre duality and Borel-Weil-Bott we will first discuss the irreducibility of the Weyl modules over a field of characteristics 0. Then moving to the prime characteristic field and we will briefly discuss the Steinberg Tensor product theorem. Finally we will wrap up the talk by browsing through some later developments and recent trends.
Here is the link to the notes of all the talks.
https://drive.google.com/file/d/1PNqfriaSWV4QbLAC9xcYuwPAu9xhjP6m/view?usp=sharing
So far the main references have been Jantzen's book ``Representation theory of Algebraic Groups'' and a note by Andersen ``Modular representation of Algebraic groups and Relations to Quantum groups''.
For this talk besides the previous references I would also like to point out the following two articles which discuss a few recent big developments in representation theory of reductive groups in prime characteristics and geometric representation theory.
1. Lectures on Geometry and modular representation theory of algebraic groups by Joshua Ciappara and Geordie Williamson
https://arxiv.org/pdf/2004.14791.pdf
2. Modular representations and reflection subgroups by Geordie Williamson
https://arxiv.org/pdf/2001.04569.pdf
- Time:
- 7:30pm
- Description:
- Speaker: Joseph Gubeladze, San Francisco State University, USA.
Date/Time: 4 March 2022, 7:30pm IST/ 2:00pm GMT / 9:00am ET (joining time
7:15pm IST).
Gmeet link: meet.google.com/xcw-ukrb-rtw
Title: Normal polytopes and ellispoids.
Abstract: Lattice polytopes are the combinatorial backbone of toric
varieties. Many important properties of these varieties admit purely
combinatorial description in terms of the underlying polytopes. These
include normality and projective normality. On the other hand, there are
geometric properties of polytopes of integer programming/discrete
optimization origin, which can be used to deduce the aforementioned
combinatorial properties: existence of unimodular triangulations or
unimodular covers. In this talk we present the following recent results:
(1) unimodular simplices in a lattice 3-polytope cover a neighborhood of
the boundary if and only if the polytope is very ample, (2) the convex
hull of lattice points in every ellipsoid in R^3 has a unimodular cover,
and (3) for every d at least 5, there are ellipsoids in R^d, such that the
convex hulls of the lattice points in these ellipsoids are not even
normal. Part (3) answers a question of Bruns, Michalek, and the speaker.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar