Talks

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The challenge is to specify how those constraints are themselves updated.

The important ingredients are two: the cotangent bundle associated to the probability simplex inherits (1) a natural symplectic structure from ED, and (2) a natural metric structure from information geometry.

The requirement that the dynamics preserves both the symplectic structure (a Hamilton flow) and the metric structure (a Killing flow) leads to a Hamiltonian dynamics of probabilities in which the linearity of the Schrödinger equation, the emergence of a complex structure, Hilbert spaces, and the Born rule, are derived rather than postulated.

 I will report on my progress, joint with David Reutter, to construct and analyze the algebraic closure of nVec – in other words, the universal n-category of framed nD TQFTs. The invertibles are Pontryagin dual to the stable homotopy groups of spheres. The Galois group is almost, but not quite, the stable PL group. An invertible TQFT can be condensed from the vacuum if and only if it trivializes on (possibly-exceptional) spheres.
 

For quantum gravity states associated to open spin network graphs, we study how the boundary (the set of open edges, which carries spin degrees of freedom) is affected by the bulk, specifically by its combinatorial structure and by the quantum correlations among the intertwiners. In particular, we determine under which conditions certain classes of quantum gravity states map bulk degrees of freedom into boundary ones isometrically (which is a necessary condition for holography). We then look at the entanglement entropy of the boundary and recover, for slightly entangled intertwiners, the Ryu-Takayanagi formula with corrections induced by the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound, a mechanism which thus leads to the rise of a black hole-like region in the bulk.

Zoom Link: https://pitp.zoom.us/j/96356007543?pwd=U2VrRlhyOThMODdMYllDMnB6VjlZQT09

The era of multi-messenger astronomy is well and truly upon us, with 90 compact binaries observed since the Advanced LIGO detectors saw first light in 2015. Despite our very own cosmic backyard, the Milky Way, being ripe with prospective sources for ground-based gravitational wave detectors, the closest source detected thus far (GW170817, the famed binary neutron star merger) was at a distance of 40 Mpc. In this talk, I will outline a number of prospective Galactic multi-messenger sources, and discuss several ways in which their detection over the next twenty years can be improved through both experimental and analytical techniques. 

Zoom Link: https://pitp.zoom.us/j/93664322641?pwd=VUoxbmFGZE1KczJ1RU1MR09TQ05Ldz09

Conformal field theories (CFTs) are ubiquitous in theoretical physics as fixed points of renormalization, descriptions of critical systems and more. In these theories the conformal symmetry is a powerful tool in the computation of correlation functions, especially in 2 dimensions where the conformal algebra is infinite. Discretization of field theories is another powerful tool, where the theory on the lattice is both mathematically well-defined and easy to put on a computer. In this talk I will outline how these are combined using a discrete version of the 2d conformal algebra that acts in lattice models. I will also discuss recent work on convergence of this discretization, as well as on applications to non-unitary CFTs that appear in descriptions of problems of interest in condensed matter physics such as polymers, percolation and disordered systems.

Zoom Link: https://pitp.zoom.us/j/95048143778?pwd=N1hhVHlsZThVYzBWTy9CNlBTUHIydz09

Logarithmic Sobolev inequalities (LSI) were first introduced by Gross in the 1970s as an equivalent formulation of hypercontractivity. LSI have been well studied in the past few decades and found applications to information theory, optimal transport, and graph theory. Recently matrix-valued LSI have been an active area of research. Matrix-valued LSI of Lindblad operators are closely related to decoherence of open quantum systems.  In this talk, I will present recent results on matrix-valued LSI, in particular a geometric approach to matrix-valued LSI of Lindblad operators. This talk is based on joint work with Li Gao, Marius Junge, and Nicholas LaRacuente.