Discrete Structures Seminar with Nika Salia – April 2
Title: Large Which Equations, Sets, (Hyper)Graphs, and Polynomials Are Extremal? Bridging Mathematical Fields Through Combinatorial Ideas
Abstract: In this talk, we will explore recent advances in combinatorics and graph theory, with a focus on stability results, extremal problems, and the structural properties of discrete objects. We will introduce a stability version of Dirac’s classical theorem, providing a full characterization of near-Hamiltonian graphs, and discuss extensions of Pósa’s theorem to hypergraphs. Additionally, I will present the resolution of a longstanding conjecture by Hakimi and Schmeichel on the maximum number of pentagons in planar graphs. Further, I will highlight connections between combinatorics and algebra, including results on intersecting families of polynomials over finite fields and higher-order extensions of Schur’s theorem. These findings illustrate the deep interplay between combinatorics and other areas of mathematics, with potential applications in both theoretical and applied settings.
Date: April 2, 2025
Time: 16:00
Location: Digital Research Lab, BSU, Main Building, 3rd floor