Number theory seminar
Tuesday, 12th December 2023, 2.30 pm
Venue: Ramanujan Hall
Host: Kummari Mallesham
Speaker: Prahlad Sharma
Affiliation: Max Planck Institute for Mathematics
Title: Counting special points on quadratic surfaces.
Abstract: We show that the modern version of the circle method powered by the equidistribution of quadratic roots allows us to count special points on quadratic surfaces. For example, we obtain asymptotic for integer points on quadratic surfaces with prime coordinates and in short intervals.
Tuesday, 12 December 2023, 4:00 PM
Venue: Ramanujan hall
Host: Harsha Hutridurga
Speaker: Trishen Gunaratnam
Affiliation: University of Geneva
Title: Tricritical phenomena in the Blume-Capel model.
Abstract: The Blume-Capel model is a ferromagnetic spin model that was
introduced in the '60s to model an exotic phase transition in uranium dioxide. Mathematically speaking, it is an Ising model coupled to a site percolation, combining two of the most beautiful models in statistical physics. It has a line of critical points - the Curie temperatures whereby the magnetisation demagnetisation transition occurs. Along this critical line, the model is expected to undergo a further phase transition at the so-called tricritical point. Despite many fascinating physics conjectures concerning the tricritical universality class, there are few rigorous results. In this talk, I will discuss these conjectures and touch upon recent results joint with Dmitry Krachun (Princeton University) and Christoforos Panagiotis (University of Bath) in establishing the existence of a tricritical phenomenon in all dimensions.