Wed, May 29, 2024
Public Access

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May 2024
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11:00am [11:30am] Brahadeesh Sankarnarayanan, IIT Bombay

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.

4:00pm [4:00pm] Roy Joshua, Ohio State University

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 K-theory
and motivic cohomology.