Spring 2025
SL2503: Tilings on surfaces#
- Speaker: Prof. Subhojoy Gupta (IISc, Bangalore)
- Abstract: We see tiled surfaces often in daily life, and the mathematical theory of such tilings has been studied since antiquity, and has deep connections to topology, combinatorics, group theory as well as the theory of computation. I shall explain some of these connections in this expository talk, focusing on the notions of regular and semi-regular tilings, on the Euclidean plane, the hyperbolic plane and on compact oriented surfaces. I’ll mention some relatively recent results as well as some unsolved problems. This talk will be accessible to a wide audience.
- Video: [TBU]
- Date and Time: Saturday, 25th October 2025, 11:00 AM - 12:30 PM
- Venue: 2nd Floor Auditorium, Academic Building
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: [1] P. Erdős, F. Herzog, G. Piranian, Metric properties of polynomials, J. Analyse Math. 6 (1958), 125–148.
- Date and Time: Tuesday, 14th January 2025, 5:30 PM - 7:30 PM
- Venue: 2nd Floor Auditorium, Academic Building