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Special Lectures 2025

Table of Contents
Spring 2025

SL2502: Infinitary Graph Ramsey Theorem and Applications #

  • Speaker: Abhishek Khetan (PostDoc, IISc, Bangalore)
  • Abstract: The infinitary graph Ramsey theorem is a fundamental theorem in Ramsey theory and has a wide range of applications (usually unexpected). In this talk we will prove the theorem and look at applications to analysis, geometry and number theory. Time permitting, we will disprove Fermat’s last theorem modulo large primes.
  • References: [TBU]
  • Date and Time: Thursday, 16th January 2025, 5:30 PM - 7:30 PM
  • Venue: 2nd Floor Auditorium, Academic Building

SL2501: Introduction to Polynomial Lemniscates #

  • Speaker: Subhajit Ghosh (PostDoc, ISI, Bangalore)
  • Abstract: A lemniscate of a complex polynomial (Q*{n}) is a sublevel set of its modulus, i.e., of the form (\left{z \in \mathbb{C}:\left|Q*{n}(z)\right|< t\right}) for some (t>0). The study of lemniscates was pioneered by Erdős, Herzog, and Piranian in [1], where they asked various questions regarding the geometric and topological properties of a unit lemniscates (i.e. for (t=1) ). In this talk, we will explore several geometric and analytic properties of polynomial lemniscates, discuss intuitive examples (\left(p(z)=z^{n}, z^{n}-a^{n}\right)) to build a foundation and address open problems concerning the area, length, and number of connected components of lemniscates. If time permits, we will extend our discussion to the realm of random polynomial lemniscates.
  • References: [TBU]
  • Date and Time: Tuesday, 14th January 2025, 5:30 PM - 7:30 PM
  • Venue: 2nd Floor Auditorium, Academic Building