Talks

The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention briefly their historical importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant: why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of surfaces of Bill Thurston and the open problems in higher dimensions. I will finish by mentioning two recent papers, one in math and the other in physics, which greatly simplify the derivations of important identities by using the theorems.

Zoom Link: https://pitp.zoom.us/j/96748003059?pwd=aElYTlNXVlY4dEhtcmd0YUcvOHZIdz09

The past decade has seen an explosion of research into resource theories—simple, quantum-information-theoretic models for constrained agents. Resource theories have provided foundational insights about thermodynamics, entanglement, and more. Yet whether resource theories can inform science outside our neighborhood of quantum information theory has been an outstanding question. I will present what is, to my knowledge, the first application of a resource theory to answer a pre-existing question in another field. Molecular switches, or photoisomers, surface across nature and technologies, from our eyes to solar-fuel cells. What probability does a switch have of switching? A general answer defies standard chemistry tools, as photoisomers are small, quantum and far from equilibrium. I will bound the switching probability by modeling a photoisomer within a thermodynamic resource theory. This work has helped pave the path for resource theories to impact science broadly.

References
• NYH and Limmer, Phys. Rev. A 101, 042116 (2020). https://journals.aps.org/pra/
abstract/10.1103/PhysRevA.101.042116
• NYH, in Eddington, Wheeler, and the Limits of Knowledge, Eds. Durham and
Rickles, Springer (2017) arXiv:1509.03873.

Zoom Link: https://pitp.zoom.us/j/99315796008?pwd=dDJBMjR2ckRmdlhtdWJZeHJuNUI1QT09

In this talk, I will discuss the duality between the two-dimensional type 0B string theory and its dual matrix quantum mechanics. This duality has been a source of motivation and a useful toy model to explore many new features of string theory. I will first revisit the computation of closed string scattering amplitudes in string perturbation theory, using new numerical methods to compute Virasoro conformal blocks in 2d supersymmetric conformal field theories. Then, I will describe a worldsheet formalism to include non-perturbative corrections to closed string scattering amplitudes, mediated by D-instantons. This formalism is of general applicability, and can be straightforwardly implemented in other string models. In the type 0B string theory, this will allow us to extend the duality dictionary beyond perturbation theory.

The possibility of having DM (or a fraction of it) charged under a dark U(1) which mixes with the U(1)EM has been of interest for many years. Many different experiments search for such a millicharged DM (MCDM), under the assumption that its velocity would be distributed according to MB. However, our galaxy and local environment have a variety of effects that make this assumption highly non trivial. In this talk, I will discuss the effects of galactic magnetic fields, collisions with Cosmic rays, acceleration from Supernovae remnants, and energy losses due collisions with particles in the interstellar medium on the velocity distribution of MCDM outside the solar system. Furthermore, to arrive at an underground detector, the MCDM would need to pass through the solar wind, not be deflected by earth's magnetic field, and pass through earth's crust to reach the underground lab. We will discuss these effects as well. I will end the talk by discussing the importance of these effects on Direct Detection experiments, and whether MCDM could explain the XENON excess.

Zoom Link: https://pitp.zoom.us/j/92701168758?pwd=UlY5Smlrd1MzWmI4ZkNyNVI5d3JIUT09

The disk of the Milky Way comprises some 100 billion stars on nearly circular orbits about the Galactic centre. Over the next few years, the Gaia Space Telescope will measure positions and velocities for over 1% of these stars. By combining equilibrium models of the Galaxy with these observations we can construct the Galactic rotation curve, which allows us to infer the large-scale structure of the dark matter halo. We can also construct a model for the mass distribution in the Solar Neighbourhood, which allows us to infer the local density of dark matter.  However, even a cursory study of the Milky Way reveals structures that signal a departure from equilibrium. The most prominent of these are the Galactic bar, spiral arms, and warping of the outer disk.  I will describe recent observations of some more subtle departures from equilibrium and discuss ways in which these observations can lead to refined models of the Galaxy and a more complete picture of the Galaxy's dynamics.

Zoom Link: https://pitp.zoom.us/j/98802402146?pwd=K3RPYlNMR2hMcXFMUm5SclU3djdiZz09

Magic-angle (θ=1.05∘) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f- and c-electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f-electrons coupled to nearly free topological semimetallic c-electrons - we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations and the minima of the charge gap at the Γ point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG. All the model’s parameters are analytically derived.