Seminars

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.

In this talk, we will discuss the integrable structure of a CFT with an extended W_3 symmetry algebra. These systems are expected to have infinitely many conserved local integrals of motion, known as quantum Boussinesq (Q.B) charges, which are in involution with each other. We will propose a prescription to systematically construct the conserved currents of such a system by combining two approaches. First, we will determine the eigenvalues of Q.B charges on the highest-weight state, the first excited state and the second excited state using the ODE/IM correspondence. Second, we will compute thermal correlators of these charges using the Zhu recursion relation, evaluating traces of composite operators composed of the energy-momentum tensor, spin-3 fields W, and their derivatives on the higher-spin module of a torus. By combining these results, we will derive new currents of the quantum Boussinesq hierarchy.

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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