


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 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/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
====================
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.