We were privileged and delighted to host world renowned mathematician and computer scientist János Pach, EPFL, Lausanne and Rényi Institute, Budapest for a seminar on Monday, 22 April, 2024 from 3:00 pm to 4:00 pm at Swami Saradananda Hall, RKMVERI, Belur.

János Pach is the recipient of multiple international awards in his illustrious career so far, such as the Grünwald Medal of the János Bolyai Mathematical Society and the Ford Award from the Mathematical Association of America, among others. He has been the program chair of several international conferences and symposia and serves on the editorial boards of several reputed journals.

Speaker: János Pach, EPFL, Lausanne and Rényi Institute, Budapest
Title of the Seminar: And what if they are not perfect?

It will primarily be expository in nature aimed for PG-level students.

Abstract:

The chromatic number of every graph is at least as large as its clique number. For perfect graphs, these two numbers coincide. Most graphs are far from perfect, but many geometrically defined graphs are “nearly perfect” in the following sense: their chromatic numbers are bounded by a function f of their clique numbers. How far these graphs are from being perfect, can be measured by the growth rate of f. After giving a whirlwind tour of the subject, we outline the proofs of some new results related to arrangements of curves in the plane, and we mention some open problems.