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: Semi-simple groups of rank one

Abstract: We prove that a connected, semi-simple 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/b-intersecting family
over [n] be? This notion was introduced in Balachandran邦athew邦ishra
(Electron. J. Combin. 26 (2019), #P2.40), wherein they showed that |F|<
O(n log n), and they gave constructions of a/b-intersecting families of
size at least O(n). The conjecture (which is still open) is that |F|<O(n)
for any a/b-intersecting 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 K-theory
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 non-existence 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 

Semi-simple Lie algebra, called the Bala-Carter theory, following the book 

of Collingwood and McGovern.

Speaker: Deep Makadia