Scattering amplitudes play a central role in understanding fundamental interactions, offering a unifying framework for both quantum field theory and quantum gravity. In this seminar, I will present my research on perturbative and non-perturbative aspects of scattering amplitudes, focusing on two main directions. On the perturbative side, I will show how soft graviton theorems, which capture universal features of the gravitational S-matrix, determine the low-frequency behavior of gravitational radiation in the classical limit. I will outline how these results enable the derivation of waveforms for general classical scattering processes and explore their implications for gravitational tail memory effects, as well as their potential observational signatures in current gravitational-wave experiments. On the non-perturbative side, I will describe how S-matrix, form factor, and spectral density bootstrap techniques can be used to constrain renormalization group flows, providing new tools to study strongly coupled quantum field theories through principles such as unitarity and analyticity. This framework offers insights into the structure of renormalization group flows in both Lorentz-invariant and Lorentz-violating systems, particularly those connecting conformal field theories in the ultraviolet to gapped phases in the infrared.

We begin by overviewing generalised symmetries in quantum field theories. We then look for its applications in 2D CFTs. We present a comprehensive symmetry resolution of entanglement entropy in rational CFTs with categorical non-invertible symmetries. This involves resolving entanglement with respect to anyonic charged sectors, labelled by irreducible representations of a modular fusion category that characterizes the symmetry. Using the associated (2+1)-D symmetry topological field theory, we define generalized, boundary-dependent charged moments and demonstrate that — unlike the group-like invertible case — entanglement equipartition across charged sectors is broken at next-to-leading order in the UV cutoff.

TBA

Many of today's significant challenges, from organizing massive datasets to identifying similar points in large datasets or calculating the similarity between DNA sequences, rely on solving fundamental computational problems. As datasets grow in size, a common strategy is to relax the requirement for an exact solution and instead use an approximation algorithm to gain a significant speedup. My research addresses this from a theoretical standpoint. By studying the hardness of approximation, my work helps establish the fundamental limits of this speed–accuracy trade-off, clarifying for key problems when we cannot significantly improve upon the performance of known algorithms, even when allowing approximate solutions. In this talk, I will present my contributions to this area through two key research programs. First, I will address problems traditionally considered solvable in polynomial time, such as computing the closest pair of points in large-scale data or finding a set cover of fixed size, a task that routinely arises in computational proteomics and peptide identification. My work in fine-grained and fixed-parameter complexity shows that, for some of these core problems, no approximation algorithm can offer a significant asymptotic speedup over exact methods. Second, I will turn to NP-hard geometric optimization problems such as clustering and Steiner tree, which are central to machine learning, logistics, and network design. For these problems, approximation algorithms are unavoidable. My work advances the understanding of the ultimate limits of approximation of these problems by proving strong inapproximability results. Zoom Link: Join Zoom Meeting https://zoom.us/j/99598370034 Meeting ID: 995 9837 0034 Passcode: 941422