


Algebraic Groups Seminar
Tuesday, May 28, 2024, 4 pm
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Venue: Ramanujan Hall
Host: Shripad M. Garge
Speaker: Saad
Affiliation: IIT Bombay, Mumbai
Title: Semisimple groups of rank one
Abstract: We prove that a connected, semisimple group of rank one is
isomorphic to SL(2) or PSL(2).
Speaker: Brahadeesh Sankarnarayanan
Day/Date/Time: 29th May, 2024, Wednesday, 11:30 AM
Venue: Ramanujan Hall
Title: Sunflowers, symmetric designs and tournaments
Abstract: For a fraction a/b in (0,1), a family F of subsets of [n] := {1,
..., n} is called a "fractional (a/b)intersecting family" if, for every
pair of distinct sets A, B in F, we have A \cap B = a/b A or a/b B.
The natural extremal question is: How large can an a/bintersecting family
over [n] be? This notion was introduced in Balachandrané‚¦athewé‚¦ishra
(Electron. J. Combin. 26 (2019), #P2.40), wherein they showed that F<
O(n log n), and they gave constructions of a/bintersecting families of
size at least O(n). The conjecture (which is still open) is that F<O(n)
for any a/bintersecting family F over [n]. In this talk, I will discuss
some recent progress on this conjecture, and some related questions
concerning ranks of certain matrix ensembles, tournaments, symmetric
designs, and sunflowers.
Wednesday, May 29, 2024, 04.00 pm
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Venue: Ramanujan Hall
Host: Sudhir R. Ghorpade
Speaker: Roy Joshua
Affiliation: Ohio State University
Title: An overview of transfer techniques in cohomology theories
Abstract: In this talk I will give an overview of transfer techniques in various
types of cohomology theories. We will begin with a leisurely review of
such techniques from algebraic topology. We will then discuss similar techniques and results in
the cohomology of algebraic varieties. The cohomology theories we consider
will range from singular cohomology of topological spaces to algebraic Ktheory
and motivic cohomology.
Date: Friday, 31st May 2024
Time: 4pm to 5pm
Venue: Ramanujan Hall
Speaker: Debaditya Raychaudhury, University of Arizona
Title: Ulrich subvarieties and nonexistence of low rank Ulrich bundles on complete intersections
Abstract: We characterize the existence of an Ulrich vector bundle on a variety $X\subset{\bf P}^N$ in terms of the existence of a subvariety satisfying certain conditions. Then we use this fact to prove that $(X,\mathcal{O}_X(a))$ where $X$ is a complete intersection of dimension $n\geq 4$, which if n = 4, is either ${\bf P}^4$ with $a\geq 2$, or very general with $a\geq 1$ and not of type (2), (2, 2), does not carry any Ulrich bundles of rank $r\leq 3$. Work in collaboration with A.F. Lopez.
The seminar of Dipendra Prasad on Algebraic groups will continue on Friday
at 4:00 pm in Room # 105. We turn to classification of nilpotent elements in a
Semisimple Lie algebra, called the BalaCarter theory, following the book
of Collingwood and McGovern.
Speaker: Deep Makadia