Mathematical Physics and Harmonic Analysis Seminar

Date: March 3, 2023

Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Lim Yen Kheng, Xiamen University Malaysia

Title: Solving physics problems from the perspective of (tropical) algebraic geometry

Abstract: In the first part of the talk, it will be shown how the partition function in statistical mechanics can be interpreted as an algebraic variety. In accordance to earlier literature, the zero-temperature limit is equivalent to taking the tropical limit of the algebraic variety. Previous literature have also generalised the temperature parameter to an n-vector. Here, we show that in the case of n=2, the two components of this generalised quantity are the inverse temperature and inverse temperature times chemical potential, respectively. Other values of n can also be similarly interpreted as various intensive thermodynamic parameters. The second part of the talk concerns null geodesics in four dimensional spacetimes. In particular, we observe that the condition for null circular orbits defines an A-discriminantal variety. A theorem by Rojas and Rusek for A-discriminants leads to the interpretation that there are two branches of null circular orbits for certain classes of spacetimes. A physical consequence of this theorem is that light rings around generic black holes with non-degenerate horizons are unstable. [Joint work with Mounir Nisse]