Seminars

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.

The talk will highlight some Science and Astronomy outreach activities undertaken by IUCAA, that have local as well as national reach. Given the challenge of the economic conditions in most of the country I will also share the low-cost approach of these and the effectiveness over the years.

The talk will explore the cyclical events that occur in a tree through the changing seasons and how we associate with them. It will also highlight the importance of long-term tree observations in understanding the effects of climate change on trees. Additionally, the discussion will emphasize how studying trees can serve as a valuable educational tool for gaining a deeper understanding of the natural world around us. This talk will draw from the work of SeasonWatch (https://www.seasonwatch.in/), an India-wide citizen science program that monitors fruiting, flowering and leaf-flush in trees to study the changing seasons.

In order to canonically realize the generalised BMS algebra at null infinity in asymptotically flat spacetimes, the celestial metric should be treated as a dynamical variable. This motivates us to consider an extension of the standard gravitational phase space defined in 2202.06691[gr-qc]. We find the Poisson brackets associated with this phase space by posing the problem as a set of second-class constraints to be solved within a simpler "kinematical" phase space, followed by a detailed constraint analysis.

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.) The meeting will be in hybrid mode. The zoom link for this meeting is as follows: Join Zoom Meeting https://zoom.us/j/99598370034 Meeting ID: 995 9837 0034 Passcode: 941422

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