Scientific Series

This talk will consider a stochastic multiple-timescale dynamical system modeling a biological neuron. With this model, we will separately uncover the mechanisms underlying two different ways biological neurons encode information with stochastic perturbations: self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR). We will then show that in the same weak noise limit, SISR and ISR are related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the model’s critical manifold.  This mathematical result could explain the experimental observation where neurons with identical morphological features sometimes encode different information with identical synaptic input. Finally, if time permits, we shall discuss the plausible applications of this result in neuro-biologically inspired machine learning algorithms, particularly reservoir computing based on liquid-state machines.

Zoom link:  https://pitp.zoom.us/j/94345141890?pwd=aTRFM3M0a0xCOEM3aXZjY2hFYzVrQT09

One of the exciting new frontiers in cosmology and structure formation is the Epoch of Reionization (EoR), a period when the radiation from the early stars and galaxies ionized almost all gas in the Universe. This epoch forms an important evolutionary link between the smooth matter distribution at early times and the highly complex structures seen today. Fortunately, a whole slew of instruments that have been specifically designed to study the high-redshift Universe (JWST, ALMA, Roman Space Telescope, HERA, SKA, CCAT-p, SPHEREx), have started providing valuable insights, which will usher  the study of EoR into a new, high-precision era. It is, therefore, imperative that theoretical/numerical models achieve sufficient accuracy and physical fidelity to meaningfully interpret this new data. In this talk, I will introduce the THESAN simulation framework that is designed to efficiently leverage current and upcoming high redshift observations to constrain the physics of reionization. The multi-scale nature of the process is tackled by coupling large volume (~100s Mpc) simulations designed to study the large-scale statistical properties of the intergalactic medium (IGM) that is undergoing reionization, with high-resolution (~ 10 pc) simulations that zoom-in on single galaxies which are ideal for predicting the resolved properties of the sources responsible for it. I will discuss applications from the first set of papers, including predictions for high redshift galaxy properties, the galaxy-IGM connection, Ly-α transmission and back reaction of reionization on galaxy formation. I will finish by highlighting recent improvements to the model and proposed future work.

Zoom link:  https://pitp.zoom.us/j/94595023029?pwd=b0c0MVZHZ01rQnprS1ZCSzVIZktqUT09

A factorization algebra is a cosheaf-like local-to-global object which is meant to model the structure present in the observables of classical and quantum field theories. In the Batalin-Vilkovisky (BV) formalism, one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible Poisson bracket of cohomological degree +1. Given a ``sufficiently nice'' such factorization algebra on a manifold $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$. The aim of the talk is to explain the sense in which the latter factorization algebra ``knows all the classical data'' of the former. This is the bulk-boundary correspondence of the title. Time permitting, we will describe how such a correspondence appears in the deformation quantization of Poisson manifolds.

Zoom Link: https://pitp.zoom.us/j/96701822187?pwd=NDh5ZFpGZ2JCNmVNOVVIYzVPV2wvdz09

Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/95685877198?pwd=ZVhaRmMrQ1VNcXNVOEpTOHVTd1F6QT09

Do the postulates of quantum mechanics survive in quantum gravity? The probabilistic interpretation of amplitudes, enforced by the unitarity of time evolution, is not guaranteed within the path integral formulation and has to be checked. Leveraging the gravitational path integral, we find a non-perturbative mechanism whereby a sum over smooth geometries leads to isometric rather than unitary evolution, which we demonstrate in simple models of de Sitter quantum gravity. These models include Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant. In these models we find that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S-matrix.

Zoom Link: https://pitp.zoom.us/j/99363952517?pwd=bm80NzhTRUtwLzQ0YjNBTkFpWVpOdz09

The formation of Primordial black holes is naturally enhanced during the quark-hadron phase transition, because of the softening of the equation of state: at a scale between 1 and 3 solar masses, the threshold is reduced of about 10% with a corresponding abundance of primordial black significantly increased by more than 100 times. Performing detailed numerical simulation we have computed the modified mass spectrum for such black holes. Making then a confutation with the LVK phenomenological models describing the GWTC-3 catalog, it is  shown that a sub-population of primordial black black holes formed in the solar mass range is compatible with the current observational constraint and could explain some of the interesting sources emitting gravitational waves detected by LIGO/VIRGO in the black hole mass gap, such as GW190814, and other light events.

Zoom Link:https://pitp.zoom.us/j/94805744664?pwd=Z3oyd05YWVlwenI5NFV6bFZOYUR0dz09

The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three 'purely even' examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups on Z/2-graded Hilbert spaces. We explain this classification, its connection to Clifford algebras, and some of its implications.

Zoom Link: https://pitp.zoom.us/j/96451287888?pwd=dlp2eVhKVTU0L2hqN2UxMy95V21SQT09

Isolated quantum systems, investigated a century ago, exhibit coherent, unitary dynamics. When such a system is coupled to an environment, the resulting loss of coherence is modeled by completely positive, trace preserving (CPTP) quantum maps for the density matrix. A lossy atom, when it has not decayed, exhibits a coherent dynamics that is in a distinct, new class. Non-Hermitian Hamiltonians with parity-time symmetry govern this class and exhibit exceptional-point (EP) degeneracies with topological features. After a historical introduction to PT symmetry, I will present examples of coherent, quantum dynamics in the static and Floquet regimes for such systems with a superconducting transmon (Nature Phys. 15, 1232 (2019)), ultracold atoms (Nature Comm. 10, 855 (2019)), and integrated quantum photonics (Phys. Rev. Res. 4, 013051 (2022); Nature 557, 660 (2018)) as platforms. These include topological quantum state transfer, entanglement/coherence control, and super-quantum correlations. I will conclude with speculations on applicability of these ideas to quantum matter, particle physics, and strong gravity. 

(* with Anthony Laing group, Kater Murch group, Le Luo group, Sourin Das group).

Zoom link:  https://pitp.zoom.us/j/92391441075?pwd=QmRYSnYveUZCci9QZFcwUHBFS29QZz09

The path integral over reparametrization modes in one dimension played an important role in the duality between JT gravity and the SYK model. In this talk, I will explain that the reparametrization modes are important also in certain computations involving the string worldsheet with boundaries. A few cases in which it is expected to play a crucial role are the Wilson loop expectation value in confining string, open strings with massive endpoints, and the string dual to the half-BPS Wilson loop in N=4 supersymmetric Yang-Mills. After reviewing these cases briefly, I will focus on the last case and explain how to compute the correlation function on the BPS Wilson loop from the string worldsheet in the conformal gauge. In particular, I will show that the inclusion of the reparametrization modes is crucial for reproducing the answer obtained previously in the static gauge. I will then use the reparametrization mode path integral to study the four-point functions in the out-of-time-ordered configuration and obtain an exact answer in a double-scaling regime interpolating between the Lyapunov regime and the late-time exponential decay. Interestingly the result has exactly the same functional form as in JT gravity although the actions for the reparametrization modes are different.

Zoom link:  https://pitp.zoom.us/j/99063427266?pwd=aG5iTlczNWhxdE9xNEZoVTlMSnVOQT09

The theory of polynomial optimisation considers a polynomial objective function subject to countable many polynomial constraints. In a seminal contribution Navascués, Pironio and Acín (NPA) generalised a previous result from Lassere, allowing for its application in quantum information theory by considering its non-commutative variant. Non-commutative variables are represented as bounded operators on potentially infinite dimensional Hilbert spaces. These infinite-dimensional non-commutative polynomials optimisation (NPO) problems are recast as a complete hierarchy of semidefinite programming (SDP) relaxations by a suitable partitioning of the underlying spaces.

The reformulation into convex optimisation problems allows for numerical analysis. We focus on an operator theoretical approach to the NPA hierarchy and show its equiv-
alence to the original NPA hierarchy. To do so, we introduce the necessary mathematical preliminaries from operator algebra theory and semidefinite programming. We conclude by showing how certain relations on operators translate to SDP relaxations yielding drastically reduced problem sizes.

Zoom Link: https://pitp.zoom.us/j/98583295694?pwd=SlcvNG90RzFrODBKSHNaUi84bG9DZz09

Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/95212522185?pwd=eWx4R3o3cmZISmtPY0xwMmdxc2EzZz09

We investigate the ground states of spin-S Kitaev ladders using exact analytical solutions (for S=1/2), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer S, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer S, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer S we find a transition between two distinct SPT orders, and for integer S we find unnecessary first order phase transitions within a trivial phase

Zoom link:  https://pitp.zoom.us/j/96692976298?pwd=d3dieERwTHJ2MEh5NFF2bFpnS3hOUT09