Seminars

TBA

Total variation distance is a fundamental distance metric for quantifying the divergence between probability distributions. It plays a central role in a wide range of areas, including statistics, information theory, machine learning, and beyond. Despite its importance, the computational aspects of total variation distance have remained relatively underexplored. In this talk, I will present our ongoing work on computing total variation distance between distributions defined over finite sample spaces.

The talk shall begin by introducing ‘groupoids’, the objects which generalise groups as well as spaces simultaneously. Fundamental groupoid appears as one of the first examples of groupoids. I shall describe the topology on the fundamental groupoid that makes the composition and inversion continuous. The point-set topolgy of this groupoid will be discussed briefly. Furthermore, we will provide necessary and sufficient condition for equipping the fundamental groupoid with a Haar system. As a final product, we shall justify existence of the C∗-algebra of this groupoid. Now the C∗-algebra of this groupoid can be described using the equivalences of groupoids. Depending on the availability of time and interest of the audience, I may describe an action category of fundamental groupoids that identifies itself with covering spaces.

In this talk, we explore the number of distinct squarefree parts in the discriminants of polynomials of the form $f(t) = t^n + c(at^k + b)^m $ with integer coefficents where $ n > mk $. We provide lower bounds in terms of the degree and coefficients. As an application of distinct squarefree parts of discriminants, we establish a lower bound on the number of such polynomials which are monogenic or have Galois group $ S_n $. This is joint work with Anuj Jakhar and Srinivas Kotyada. This is a pre-synopsis talk.

In this talk, I will speak about our work on Nonassociative Polynomial Identity Testing. We give the first efficient polynomial identity testing algorithms over the nonassociative polynomial algebra. In this setting, multiplication among the formal variables is commutative but it is not associative. This complements the strong lower bound results obtained over this algebra by Hrubeš, Yehudayoff, and Wigderson and Fijalkow, Lagarde, Ohlmann, and Serre from the identity testing perspective. Our main results are the following: 1) We construct nonassociative algebras (both commutative and noncommutative) which have no low degree identities. As a result, we obtain the first Amitsur-Levitzki type theorems over nonassociative polynomial algebras. As a direct consequence, we obtain randomized polynomial-time black-box $\pit$ algorithms for nonassociative polynomials which allow evaluation over such algebras. 2) On the derandomization side, we give a deterministic polynomial-time identity testing algorithm for nonassociative polynomials given by arithmetic circuits in the white-box setting. Previously, such an algorithm was known with the additional restriction of noncommutativity. 3) In the black-box setting, we construct a hitting set of quasipolynomial-size for nonassociative polynomials computed by arithmetic circuits of small depth. Understanding the black-box complexity of identity testing, even in the randomized setting, was open prior to our work. (Based on Joint work with Partha Mukhopadhyay and C. Ramya, to appear in RANDOM 2025)

TBA

Many quantum protocol discovery problems can be formulated as closed- or open-loop control tasks, such as those for quantum error correction (QEC) and quantum gate design. Highlighting a QEC protocol as an example, I will explain how the problem of feedback control naturally adapts to the workflow of reinforcement learning (RL) – a discipline of machine learning typically used in technological applications like self-driving cars. Through some of the earliest works on RL applications in quantum physics, we have found that such techniques can be useful for designing protocols for steering quantum systems toward desired goals, especially when used as an add-on to theoretical formulations. After briefly highlighting those early works and the current state of the art in this emerging field, I will present my latest works, where theoretical protocols for fast and high-fidelity quantum gate construction were shown to be improved through RL-discovered, non-intuitive protocols, demonstrating its importance in quantum computing.

The goal of the talk is to discuss some recent applications of quantum and quantum-inspired interferometry in the fields of imaging and quantum state measurement. In the first part of the talk, I will highlight three imaging techniques that rely on three types of optical interference. The first imaging technique allows us to obtain object-information at spectral ranges for which adequate detectors are not available. The second imaging technique is immune to time-dependent phase fluctuations (noise) in an interferometer. The third imaging technique contains the features of the first two imaging techniques, i.e., it is immune to phase noise and allows to cover spectral ranges for which adequate detectors are not available. In the second part of the talk, I will touch upon a quantum interferometric approach to bipartite entanglement measurement and two-qubit state tomography. It is currently the only approach that allows us to characterize entanglement in two-photon mixed states without the detection of one of the photons.

I will argue that there is an emergent infrared triangle near the horizon of a black hole, analogous to the one in flat space. In scalar QED in a Schwarzschild background, I will show that the Ward identities corresponding to near-horizon asymptotic symmetries match with a new emergent leading soft photon theorem that can be derived in an effective field theory near the horizon. Finally, the soft factor is related to a near-horizon memory effect via a Fourier transform. I will argue that the story generalises to gravitational perturbations. Moreover, I will demonstrate the ubiquity of this structure across dimensions, in contrast to the flat space IR triangle. Time permitting, I will conclude with some speculations on a possibly emergent conformal field theory on the horizon.