Seminars

This work is motivated by the recent evidence for a double-copy relationship between open- and closed-string amplitudes in Anti-de Sitter (AdS) space. At present, the evidence has the form of a double-copy relation for string-amplitude building blocks, which are combined using the multiple-polylogarithm (MPL) generating functions. These generate MPLs relevant for all-order AdS curvature corrections of four-point string amplitudes. In this work, we prove this building-block double copy using a new, noncommutative version of twisted de Rham theory. In flat space, the usual twisted de Rham theory is already known to be a natural framework to describe the Kawai-Lewellen-Tye (KLT) double-copy map from open- to closed-string amplitudes, in which the KLT kernel can be computed from the intersections of the open-string amplitude integration contours. We formulate twisted de Rham theory for noncommutative-ring-valued differential forms on complex manifolds and use it to derive the intersection number of two open-string contours, which are closed in the noncommutative twisted homology sense. The inverse of this intersection number is precisely the AdS double-copy kernel for the four-point open- and closed-string generating functions. (Based on https://doi.org/10.1007/JHEP04(2026)112)

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

We introduce a new method to obtain lower bounds for the 2k-th moment of a broad class of L-functions for all real k>0. In particular, our method applies to families of higher degree L-functions which were previously inaccessible. https://www.imsc.res.in/~anupdixit/IMSc-CMI-NT-seminar.html

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

TBA

Out-of-equilibrium systems are ubiquitous in nature. In contrast to their equilibrium counterparts, which are fairly well-understood using the framework of statistical mechanics, a description of them is challenging and is at the forefront of current-day research. Recently, important experimental and theoretical techniques have been developed, and advances have been made in both classical and quantum systems that are out-of-equilibrium. This conference aims to discuss the current trends in this broad area of research by bringing together experts, early-career researchers, postdocs, and students working in this field. Topics would include (but are not limited to) quantum many-body scars, driven and dissipative systems, disordered, noisy setups, stochastic processes, first-passage problems, and random walks. An important goal is to bring together the community of people working on the classical and quantum fronts and foster collaborations between them. https://www.imsc.res.in/current_trends_classical_and_quantum_out_of_equilibrium_systems_ctcqoes

I will discuss the noise sensitivity of Boolean functions on the symmetric group, where the noise is generated by a Markov chain on the symmetric group. The main focus will be on comparison results between different noise sources and their applications. I will present several examples, including the result that the indicator of long cycles is noise-sensitive under the interchange process on the discrete torus in any fixed dimension.   This talk is based on recent joint work with Gideon Amir (arXiv: https://arxiv.org/pdf/2606.29829).

When a two-dimensional electron gas is cooled to cryogenic temperatures and subjected to a strong perpendicular magnetic field, the Hall resistance becomes quantized. When this quantization occurs at fractional values, it signals the fractional quantum Hall effect (FQHE), a strongly correlated phase of matter with emergent topological order. A striking consequence is the appearance of fractionally charged particles, called anyons, now observed experimentally, whose exchange can yield fractional statistics. In special FQHE states, these anyons are non-Abelian, providing a route to realizing fault-tolerant topological quantum computation. While such properties are long predicted by low-energy Chern–Simons and conformal field theory descriptions, obtaining microscopic access, directly in terms of electronic coordinates and explicit many-body wave functions, remains challenging beyond a few canonical examples. In this thesis, I develop many-body wave-function frameworks to study FQH phases, ground states, and excitations at the microscopic level. This includes analyzing both collective (neutral) excitations, Abelian and non-Abelian anyons, and connecting their properties to the underlying topological field theory. In this talk, I will give a brief overview of the above topics and then highlight a work on the construction of quasihole bases for a broad family of non-Abelian FQH states using parton wave functions. This reproduces the fusion-space dimensionality expected from their underlying conformal field theory, consistent with level-rank duality across the parton family. As an application, we numerically compute braiding matrices for representative parton states for large systems, providing a general framework for diagnosing non-Abelian characteristics in candidate FQH states.

Compartmentalization is ubiquitous in biology, enabling the spatiotemporal regulation of various biochemical processes. Historically, cells have been thought to achieve compartmentalization via membrane-bound bodies known as organelles. However, a new paradigm has recently emerged in which cells can form membraneless compartments called biomolecular condensates. In this thesis, I seek to uncover the physical principles underlying the spatiotemporal regulation of both membrane-bound and membraneless organelles. First, I will discuss the association between microtubules and tau proteins, the dysregulation of which is implicated in neurodegenerative diseases. Through a dialogue between theory and experiments, we show that tau molecules form multilayered condensates via a prewetting-like transition. These condensates promote the recruitment of tau interactors, such as tubulin and other microtubule-associated proteins, thereby allowing for various physiological functions on the microtubule surface. In related work, I will discuss how protein–protein interactions affect transcription factor (TF) target search kinetics. Timely gene expression requires TFs to locate their specific binding sites on DNA. Previous studies have shown that this search is optimized by facilitated diffusion, which combines 3D diffusion with 1D sliding. Here, we show that in the presence of TF–TF interactions, simple 3D diffusion can outperform facilitated diffusion. In line with our results, recent experiments in live cells have shown TFs locating their target sites through 3D diffusion alone. Our results highlight an alternative mechanism cells can use to accelerate target search. In the last part, I focus on membrane-bound organelles. Cells tightly regulate organelle abundances in response to external cues, but the underlying mechanisms remain unclear. We employ a theoretical model that uses time-lapse microscopy datasets to infer the mechanisms regulating organelle biogenesis. Together, this work advances our understanding of intracellular organization across membraneless and membrane-bound organelles.

TBA