Speaker :- Dr. Brahadeesh Sankarnarayanan

Title of the Talk :- Sunflowers and symmetric designs

Date, Time and venue :- 28 April 2025, 5:00 PM - 6:00 PM, Seminar Hall, Dept. of Mathematics

About the speaker :- Dr. Brahadeesh Sankarnarayanan received his BS-MS (Dual) Degree in Mathematics from IISER Bhopal, and his Ph.D. in Combinatorics from IIT Bombay. He has been an Institute Postdoctoral Fellow at IIT Bombay until February 2025. His research interests lie broadly in extremal graph theory and combinatorics. In graph theory, he has worked on colorings and list colorings of graphs, from extremal and algorithmic perspectives. In extremal combinatorics, he has worked on a fractional variant of intersecting families of set systems, using probabilistic and linear algebraic tools. His current research interests include the study of intersecting families of graphs via entropy-theoretic methods, and the study of path representations of graphs.

Abstract :- For a fraction θ = a/b ∈ (0,1), a family F of subsets of [n] := {1,...,n} is called a (fractional) θ-intersecting family if, for every pair of distinct sets A,B ∈ F, we have |A∩B| ∈ {θ|A|,θ|B|}. The natural extremal question is: How large can a θ-intersecting family over [n] be? This notion was introduced in Balachandran–Mathew–Mishra (Electron. J. Combin. 26 (2019), #P2.40), wherein they showed that |F| ≤ O(n log(n)^2), and they gave constructions of θ-intersecting families of size at least Ω(n). The conjecture (which is still open) is that |F| ≤ O(n) for any θ-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, sunflowers, and symmetric designs.