Talks

The Levin-Wen model is known to produce a vast array of topological phases of matter. Among these theories are gauge theories such as the twisted quantum double. In this talk, we will show that the Levin-Wen model is itself a gauge theory. In particular, given a unitary fusion category C, we construct a globally tube algebra (Tube(C)) symmetric lattice model and gauge this symmetry to produce the Levin-Wen model with anyons described by the Drinfeld center Z(C). This construction endows the terms of the Levin-Wen Hamiltonian with the interpretation of flux and charge operators for the Tube(C) gauge symmetry. Furthermore, this construction gives a gauge theoretic interpretation to the mathematical fact that the category of representations of Tube(C) is equivalent to Z(C). To demonstrate this new class of Tube(C) symmetric theories, we will explicitly explore the case where C is the Fibonacci category Fib. We will write down the ungauged Tube(Fib) symmetric theory, compute the symmetry action, and show how to gauge the Tube(Fib) global symmetry to produce the double Fibonacci Levin-Wen model.

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An intense beam of Standard Model (SM) particles colliding with a fixed target is one of oldest types of accelerator-based experiments. With recent interest in production and detection of relatively light, weakly-coupled (``dark sector'') states, these set-ups are again playing a central role in the search for beyond-SM (BSM) physics. Signal rate prediction is often challenging in fixed-target experiments, requiring the simulation of many SM and BSM processes as the beam particle propagates through the target. Both play a key role in determining the flux of dark sector particles through a detector. An accurate description of these fluxes is needed, since small errors in angular and energy distribution predictions can lead to significant over or under estimates of signal rate in the detector. Focusing for simplicity on BSM particle production from electromagnetic cascades, I will describe how we can model production of BSM particles, highlighting some frequently-used approximations used in the past. I will then show that improvements in both SM and BSM modelling are desirable. We implemented several of these improvements in a code, PETITE. Using this tool we can show how mismodelling of SM or BSM processes can lead to orders of magnitude difference in signal rates at realistic experimental setups.

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Feynman diagrams and the associated integrals are crucial in perturbative quantum field theory for translating theory input into concrete, observable quantities. I will talk about the fascinating interplay of physics and mathematics that emerges from the ensemble of these diagrams. From linear algebra to quantum mechanics or wave phenomena to Fourier analysis - physics and mathematics tend to regularly exchange ideas that often lead to breakthroughs on the other side. I will illustrate two new examples of such exchanges I contributed to. One exchange is from the mathematical theory of tropical geometry to evaluating intricate, physically relevant Feynman integrals that have been inaccessible before. In the second exchange, we used ensembles of Feynman diagrams and their renormalization to prove a long-standing conjecture in geometric group theory. The results give new insights into the 'dark matter'-problem in the moduli spaces of graphs and curves' cohomology.  Both these moduli spaces' cohomologies are of fundamental interest in algebraic geometry, topology and geometric group theory.

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Neural Network Field Theories (NNFTs) are field theories defined via output ensembles of initialized Neural Network (NN) architectures, the backbones of current state-of-the-art Deep Learning techniques. Different limits of NN architectures correspond to free, weakly interacting, and non-perturbative regimes of NNFTs, via central limit theorem and its violations. Nature of field interactions in NNFTs can be controlled by tuning architecture parameters and hyperparameters, systematically, at initialization. I will present a systematic construction of scalar NNFT actions, using various attributes of NN architectures, via a new set of Feynman rules and techniques from statistical physics. Conversely, I will present the construction of a class of NN architectures exactly corresponding to some interacting scalar field theories, via a systematic deformation of NN parameter distributions. As an example of the latter method, I will present the construction of an architecture for $\lambda \phi^4$ scalar NNFT. Lastly, I will introduce Grassmann NNFTs, their free and interacting regimes via central limit theorem for Grassmanns, and construction of an architecture corresponding to free Dirac NNFT. This approach provides us a way to initialize NN architectures exactly representing certain field configurations, and are useful for computing attributes, e.g. correlators, of field theories on lattice.

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I present work done in the last years on the construction of dynamical coordinate systems for highly symmetric backgrounds, such as Minkowski, de Sitter, and FLRW cosmologies, and which are needed in the relational approach to construct gauge-invariant observables in gravity. I show that it is possible to restrict the inevitable non-local contributions to the past light cone such that the obtained observables are causal. Lastly, I present some applications, namely the leading quantum gravitational corrections to the local expansion rate of our universe (the Hubble rate) and the Newtonian gravitational potential.

Based on arXiv:1711.08470, arXiv:1806.11124, arXiv:2108.11960, arXiv:2109.09753, and arXiv:2303.16218.

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The Langlands program is a grand organizing vision for a large slice of number theory and representation theory. A shockingly accurate metaphor for the Langlands program has emerged as electric-magnetic duality in four-dimensional gauge theory, but where the role of spacetime is played by objects from arithmetic. I will describe recent work with Yiannis Sakellaridis and Akshay Venkatesh, in which we apply ideas from QFT (the Gaiotto-Witten electric-magnetic duality for boundary theories) to a fundamental problem in number theory, predicting the relation between L-functions of Galois representations and integrals of automorphic forms.

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What happened in the earliest moments of the Universe? Despite decades of theoretical and observational work, a detailed understanding of the primordial Universe has remained elusive. In this talk, I will show how surveys of millions of galaxies can shed new light on these issues by constraining the statistics of the Universe just after inflation. By combining robust perturbative models with novel numerical techniques, I have placed some of the first (non-Gaussian) constraints on the dynamics and field content of inflation from galaxy surveys; these will sharpen considerably in the next decade as the volume of observational data grows. Through a combination of traditional perturbative approaches and new symmetry-based techniques, I will demonstrate how current and future galaxy surveys can be used to search for a wealth of new physics, including primordial scattering processes and parity violation, opening the door to constraining ultra-high-energy physics with low-energy data.

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Horizons of black holes in equilibrium and null infinity of asymptotically flat space-times are null 3-manifolds but have very different physical connotations. We first show that they share a large number of geometric properties, making them both weakly isolated horizons. We then use this new unified perspective to unravel the origin of the drastic differences in the physics they contain. Interestingly, the themes are woven together in a manner reminiscent of voices in a fugue.The talk is based on joint work with Simone Speziale (arXiv:2401.15618 and arXiv 2401:????).

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