Talks

In general, observables in QFTs can only be computed perturbatively using Feynman integrals. In this talk, which is based on arXiv:2008.12310 and arXiv:2204.06414, I will address some questions on the computability of such observables. By looking at QFT through the lens of tropical geometry, one can see that the runtime of such computations is dominated by the time it takes to understand the structure of certain polytopes. In the case of scalar QFTs on Euclidean space the relevant polytopes turn out to be generalized permutahedra, whose structure is well-understood thanks to the works of Postnikov, Aguiar and Ardila.  Using these insights, results in a new algorithm for Feynman integral evaluation that exceeds the capabilities of existing methods by multiple orders of magnitude, while being easy to implement.  I will also briefly discuss current wip that extends these findings to QFTs on Minkowski spacetime.

Zoom link:  https://pitp.zoom.us/j/93629580865?pwd=WnJ6aUVpckFZWGVDL0NqMTFrWlhBQT09

The long range nature of gravity complicates the dynamics of self-gravitating many-body systems such as galaxies and dark matter (DM) halos. Relaxation/equilibration of perturbed galaxies and cold dark matter halos is typically a collective, collisionless process. Depending on the perturbation timescale, this process can be impulsive/fast, adiabatic/slow or resonant. First, I shall present a linear perturbative formalism to compute the response (in all three regimes) of disk galaxies to external perturbations such as satellite impacts. I shall elucidate how phase-mixing of the disk response gives rise to phase-space spirals akin to those observed by Gaia in the Milky Way disk, and how these features can be used to constrain the Milky Way’s potential as well as its dynamical history. Next, I shall discuss the secular evolution of a massive perturber due to the back reaction of the near-resonant response of the host galaxy/halo. In this context I shall present two novel techniques to model the secular torque (dynamical friction) experienced by the perturber: 1. a self-consistent, time-dependent, perturbative treatment and 2. a non-perturbative orbit-based framework. These two approaches explain the origin of certain secular phenomena observed in N-body simulations of cored galaxies but unexplained in the standard Chandrasekhar and LBK theories of dynamical friction, namely core-stalling and dynamical buoyancy. I shall briefly discuss some astrophysical implications of these phenomena: potential choking of supermassive black hole mergers in cored galaxies, and the possibility of constraining the inner density profile (core vs cusp) of DM dominated dwarf galaxies and therefore the DM particle nature.

Zoom link:  https://pitp.zoom.us/j/99089663538?pwd=aVVjV2ozMkZRTkE0ZW1Ib0dGUC9tdz09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

In this talk, I will introduce the so-called entanglement linear response, i.e., response under entanglement generated unitary dynamics. As an application, I will show how it can be applied to certain anomalies in 1D CFTs. Moreover, I will apply it to extract the quantum Hall conductance from a wavefunction and how it embraces a previous work on the chiral central charge. This gives a new connection between entanglement, anomaly and topological response. If time permits, I will also talk about how it inspires some generalizations of the real-space Chern number formula in free fermion systems.

Zoom link:  https://pitp.zoom.us/j/96535214681?pwd=MldXRkRjZ1J6WS95WXQ0cG03cWdCZz09

Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized. In particular, for certain parameters, we will show that these neural network states can look typical in their entanglement profile while still being distinguishable from a typical state by their fractal dimensions. The obtained phase diagrams may help inform the initialization of neural network ansatzes for future computational tasks.

Zoom link:  https://pitp.zoom.us/j/94316902357?pwd=RGxWYm9EWGtGYzBvUzM5ZWdwVTB5dz09

The Deligne-Mumford moduli space of genus 0 curves plays many roles in representation theory.  For example, the fundamental group of its real locus is the cactus group which acts on tensor products of crystals.

I will discuss a variant on this space which parametrizes "cactus flower curves".  The fundamental group of the real locus of this space is the virtual cactus group.  This moduli space of cactus flower curves is also the parameter space for inhomogeneous Gaudin algebras.

Zoom link:  https://pitp.zoom.us/j/96658223425?pwd=NUxRN2FsdWJ1SWtHMlRDcTdHMGNPQT09

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09