In this talk I will describe how some of the quantum mechanical behaviour near an event horizon in relativistic spacetimes can be fully captured in a condensed matter setting of applied potentials on quantum Hall systems. Through symmetry arguments, I show that the behaviour of quantum mechanical modes near a black hole can be captured by the physics of an inverted Harmonic oscillator that is realized in the quantum Hall system. The equivalence of the Lorentz boosts to area preserving shear deformations in the lowest Landau level leads to similar time-evolution of modes in the two settings, ultimately leading to the physics of Hawking radiation. The same symmetry arguments also lead to new perspectives on some quantum Hall phenomena such as the Hall viscosity. The inverted harmonic oscillator also hosts decaying modes with quantised decay rates. I show how these could be accessed in a quantum Hall set up through wave-packet scattering. I will also give a pedagogical introduction to the Hawking radiation in black holes, geared towards condensed matter audience. The talk will be based on the following two works: Phys. Rev. Lett. 123, 156802 (2019), arXiv:2012.09875 (2020). Here is the link to the google meet: meet.google.com/iez-tcrq-otu.

We will first recall Apéry's and Beukers' proofs of irrationality of zeta(2) and zeta(3) and attempt to formulate an "existential" proof of irrationality using Minkowski's linear forms theorem. We will then outline the difficulties in using several methods to estimate a determinant at the heart of this proof including multiple hypergeometric series, vector equilibrium problems, large deviations and Szegő's limit theorem. We then change the irrationality criterion to observe that one of these approaches yields the irrationality of zeta(2). The final part of the talk will be to attempt to convince the audience that a Selberg-type integral evaluation exists which will side-step all the above difficulties. Google meet link: meet.google.com/bfy-buhp-ohf

Webinar: join at https://zoom.us/j/9232575195?pwd=OGgxV29CQ1RaUDd5N3NQNWluMDhydz09 We live in a world where the quest for efficient computation is indispensable. Understanding the amount of resource (e.g., time, space) required to solve a given computational problem on models of computation (e.g., Turing machines) underlies much of *Computational Complexity Theory*. In this talk, we will primarily be interested in the complexity of computing polynomials by *arithmetic circuits* which are a natural computational model for polynomials. The number of arithmetic operations needed to compute a polynomial is captured by the *size* of an arithmetic circuit computing it. While the symbolic *determinant *polynomial can be computed by polynomial size arithmetic circuits, Valiant(1979) conjectured that the symbolic *permanent *cannot be. Despite consistent efforts, the best-known circuit size lower bound is barely super-linear in the number of variables. Given that determinant, permanent are all multilinear polynomials, understanding multilinear computation is of significant importance. We will briefly discuss some results in this direction. Most known lower bounds can be unified under the framework of *algebraically natural proofs* introduced by Grochow, Kumar, Saks, Saraf(2017) and Forbes, Shpilka, Volk(2018). We will review this natural recipe for proving arithmetic circuit size lower bounds. While some believe that this framework cannot be extended to settle the truth of Valiant’s conjecture, some of our recent results highlight the existence of *natural lower bound techniques* for proving lower bounds against certain rich subclasses of arithmetic circuits. En route, we will briefly discuss other interesting computational problems concerning polynomials such as *polynomial identity testing, **circuit reconstruction *and* matrix rigidity*.

I will discuss a novel formulation of relativistic magnetohydrodynamics that describes the low-energy behaviors of a fluid in a dynamical magnetic field. This is done in a way faithful to the symmetries of the system, i.e., conservations of the energy-momentum and of the magnetic flux from the magnetic one-form symmetry. I will also discuss an extension to the systems with chirality imbalances and a new helical instability emerging there as a solution of the chiral magneto hydrodynamics.