Seminars

A long time ago, Newman and Janis showed that a complex transformation of the Schwarzschild solution leads to the Kerr solution. The Newman-Janis (NJ) algorithm on the space of classical solutions in GR and electromagnetism can be used in scattering amplitudes to map an amplitude with external scalar states to the one associated with the scattering of “infinite spin particles”. The minimal coupling of these particles to the gravitational or electromagnetic field corresponds to the classical coupling of the Kerr black hole with linearized gravity or the so-called $\sqrt{Kerr}$ charged state with the electromagnetic field. In this talk, I will discuss the idea of the NJ algorithm on the space of scalar QED amplitudes to compute classical observables such as the angular momentum impulse and the radiative field in the electromagnetic scattering of $\sqrt{Kerr}$ objects (analog of Kerr black holes in electromagnetism) at leading order in the coupling, via the Kosower, Maybee, O’Connell (KMOC) formalism. I will also discuss the relevance of the infinite hierarchy of the soft factorization theorems for gravitational tree-level amplitudes in the context of such classical (gravitational) scattering processes in four spacetime dimensions.

Majorana fermions are the particles of their own antiparticle that manifest as zero-energy quasiparticles in topological superconductors, exhibiting non-Abelian exchange statistics useful for quantum information processing. In this talk, I will introduce the basics of topological superconductors and Majorana fermions in p-wave superconductors. We model a Josephson junction with a magnetically textured barrier in a 2D p-wave superconductor, considering both px+py and px+ipy​ pairings. The magnetic barrier strength and periodicity control the number of Majorana zero modes and define three topological phases. We identify 1D Majorana edge modes (flat or dispersive) and localized end modes and hybridization of both edge and end modes through local density of states and Josephson current. A discontinuous jump in the current and a pronounced hump in the px​+ipy​ case reveal Majorana hybridization, enabling distinction between edge and end modes. Reference: arXiv: 2503.18362

The past two decades have witnessed dramatic improvements in SAT solving, enabling today's solvers to handle problems involving millions of variables. Motivated by the power of SAT solvers, there is a growing interest in tackling problems that lie in higher classes of the polynomial hierarchy, wherein NP calls are to be replaced by SAT solvers in practice. The complexity of such algorithms is measured in terms of calls to NP oracles. However, SAT solvers are not mere decision oracles: they also provide a satisfying assignment when the formula is satisfiable. Therefore, a theory based on NP oracles is limiting, and there is a need for a theory that takes into account the power of SAT solvers. In this talk, I will discuss how such consideration leads to new algorithms and new lower bounds in the context of two fundamental problems: model counting and sampling. Based on joint work (LICS-22 and ICALP-23) with Diptarka Chakaraborty, Sourav Chakraborty, Remi Delannoy, and Gunjan Kumar

We give a complete description of the eigenvalues of all permutations in irreducible representations of symmetric and alternating groups. (This talk is the speaker's pre-synopsis seminar)

Scattering amplitudes are the cornerstones of our current understanding of quantum field theories. On-shell methods offer efficient ways to calculate amplitudes in some theories and uncover beautiful structures usually obscured by the Feynman diagrammatics. The planar maximal supersymmetric (N=4) gauge theory is well suited for the use of on-shell methods, and the amplitudes have a positive geometry description in terms of the amplituhedron. We discuss the spontaneously symmetry broken N=4 super Yang-Mills theory and pure gauge theory in this talk. We study the so-called `on-shell functions' in the massive N=4 SYM, and realize the massive BCFW shifts as on-shell diagrams. We stumble upon mass deforming BCFW shifts. We discuss the maximal cut of simple loop diagrams and, using the generalized unitarity, find the loop amplitudes in massive N=4 SYM. In the second part of the talk, we discuss the pure gauge theory and realize its amplitudes from the positive geometry and combinatorics. The associahedron is a combinatorial object capturing the combinatorics of triangulations of an n-gon, and hence planar trivalent graphs. We make use of the Corolla polynomials to spin up the canonical form of the associahedron, yielding the gluon amplitudes. The similar Corolla polynomials for one loop lead us to the loop integrand of the n-gluon scattering. We use another representation of the Corolla polynomial to spin up the recently discovered curve integral formula.

We consider the setting of fair division of indivisible items and focus on the fairness notion known as "envy-freeness up to any item (EFX)". The input to the problem is a set of n agents and m items, where each agent has a valuation function defined for each subset of items. The goal is to partition the items among the agents so that the allocation satisfies the EFX requirement. Such an allocation is called an EFX allocation. When two or more agents have the same valuation function, the agents are said to have the same "type". Existence of EFX allocations is one of the central problems in fair division. EFX allocations are known to exist for three agents, for the case when there are at most two types of agents, and (partial EFX allocations) for an arbitrary number of agents, say n, with at most n-2 items left unallocated. We make progress on these three fronts and show the following: 1. EFX allocations exist when agents have at most three types. 2. EFX allocations with at most k-2 items left unallocated, when agents have at most k types. In this talk, I will highlight some techniques and challenges that arise in extending the results on EFX for agents to EFX for types of agents. (This is a joint work with Pratik Ghosal, Vishwa Prakash H.V., and Nithin’s Varma.)

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