## 16th IFS Seminar

Title: Uniqueness theorems in analysis Speaker: Armen Vagharshakyan, Institute of Mathematics, Yerevan Date: Mon 24 October 2022 Time: 3:00 PM BST / 4:00 PM CEST / 6:00 PM Yerevan / 10:00 PM Beijing Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Several theorems in analysis may be viewed as uniqueness theorems: the Shannon-Nyquist sampling theorem in signal processing, Cantor's theorem on trigonometric series, Riesz brothers' theorem in measure theory, Carlson's theorem in complex analysis. We explore the interrelations between those theorems.

## 15th IFS Seminar

Title: From orbit to particle (and its generalization) Speaker: Euihun Joung, Kyung Hee University, Seoul Date: Mon 25 July 2022 Time: 2:00 PM BST / 3:00 PM CEST / 5:00 PM Yerevan / 10:00 PM Seoul Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: I will explain how the method of coadjoint orbits, combined with the ideas of constrained Hamiltonian systems and dual pair correspondence, can give useful insights into the problem of finding relativistic particle actions and its generalizations.

## 14th IFS Seminar

Title: Recent progress in Higher Spin Gravity and three-dimensional bosonization duality Speaker: Eugene Skvortsov, U. Mons & Lebedev Inst. Date: Thu 16 June 2022 Time: 1:00 PM BST / 2:00 PM CEST / 4:00 PM Yerevan / 9:00 PM Seoul Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: I will give a general overview of one of the ideas to construct viable models of quantum gravity: Higher Spin Gravity. Via AdS/CFT correspondence certain Higher Spin Gravities turn out to be related to (Chern-Simons) vector models that describe some physical phenomena and exhibit a number of recently discovered dualities, which can be explained by higher spin symmetries. If time permits, I will dive into strong homotopy algebras that are behind some Higher Spin Gravities and also provide a new type of symmetry for conformal field theories.

## 13th IFS Seminar

Title: Amplification of Gravitational Waves in the Early Universe Speaker: Valeri Vardanyan, KAVLI IPMU (Tokyo) Date: Thu 19 May 2022 Time: 09:00 AM BST / 10:00 AM CEST / 12:00 PM Yerevan / 5:00 PM Tokyo Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: The yet undetected primordial gravitational waves are widely considered as a smoking gun for the inflationary scenario. However, low-scale inflation predicts vanishingly small amplitude for gravitational waves, hence rendering this important inflationary regime effectively untestable by observations. We propose a novel mechanism for enhancing primordial gravitational waves without significantly affecting the curvature perturbations produced during inflation. This is achieved due to nonlinear sourcing of resonantly amplified scalar field fluctuations. Our result is an explicit scale-dependent counterexample of the famous Lyth bound, which opens up a promising perspective of producing detectable inflationary tensor modes with low-scale inflation and a sub-Planckian field excursion. We explicitly demonstrate the testability of our mechanism with upcoming cosmic microwave background B-mode observations.

## 12th IFS Seminar

Title: Integrable quantum field theories - Inverse scattering, local von Neumann algebras, asymptotic completeness Speaker: Gandalf Lechner, FAU (Erlangen-Nürnberg) Date: Thu 21 April 2022 Time: 7:00 AM PDT / 3:00 PM BST / 4:00 PM CEST / 6:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: In this talk, I will review how integrable quantum field theories on two-dimensional Minkowski space can be formulated and constructed in a mathematically rigorous setting. The physical idea of our approach is that of inverse scattering theory, namely we start from a given 2-particle S-matrix S and then construct a QFT that has this prescribed scattering behaviour at 2- particle level, and factorizes at higher particle level (that is, there is no particle production). In order to avoid convergence problems of perturbative expansions we will use an operator-algebraic setting which provides us with tools (von Neumann algebras, Tomita-Takesaki theory) to decide the existence of local quantum observables associated with S without needing to construct them explicitly. In the course of the talk I will explain some of the main ideas underlying the operator-algebraic approach to QFT and compare them with other approaches. In particular, I will explain how the ideas underlying the Zamolodchikov-Faddeev algebra and asymptotic completeness can be proven in this context.

## 11th IFS Seminar

Title: The python's lunch and complexity of decoding Hawking radiation Speaker: Hrant Gharibyan, CalTech (Pasadena) Date: Thu 17 February 2022 Time: 8:00 AM PST / 4:00 PM GMT / 5:00 PM CET / 8:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: In this talk, I will focus on geometric obstructions to decoding Hawking radiation (python’s lunch). Harlow and Hayden (arXiv: 1301.4504) argued that distilling information out of Hawking radiation is computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. I will trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, I will present a conjecture that relates the computational hardness of distilling information to geometric features of the wormhole.

## 10th IFS Seminar

Title: When they go low, we go high Speaker: Ruben Minasian, Institut de Physique Théorique, CEA-Saclay Date: Wed 19 January 2022 Time: 2:00 PM GMT / 3:00 PM CET / 6:00 PM Yerevan / 10:00 PM Beijing Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: In various dimensions, there is an infinite number of supergravity models (with varying amounts of supersymmetry). A tiny fraction of these (probably a finite number) corresponds to the low energy limit of string-theoretic constructions. Does the rest teach us anything? I will try to discuss what is easy/hard in string theory/supergravity.

## 9th IFS Seminar

Title: Gibbs' Theory and Statistical Physics: A third approach to understanding the world probabilistically? Speaker: Hong Qian, University of Washington Date: Thu 18 November 2021 Time: 8:00 AM PT / 4:00 PM GMT / 5:00 PM CET / 8:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: How to apply the mathematical theory of probability to real world problems? Interpretations of "what is probability" have led to the Bayesian and frequentist schools. In very elementary terms, I try to show how Gibbs' theory stitches together both thoughts, as well as the large deviations theory, an asymptotic analysis of the law of large numbers. This yields the statistical ensemble as a parametric family of probabilistic models that are specifically informed by the nature of "observables". Two well-known entropy functions, Gibbs' and Shannon's, as well as the Pitman-Koopman-Darmois theorem, figure prominently in our theory.

## 8th IFS Seminar

Title: Energy conservation and fluctuation theorems are incompatible for quantum work Speaker: Karen Hovhannisyan, Uni Potsdam Date: Tue 19 October 2021 Time: 9:00 AM PT / 5:00 PM BST / 6:00 PM CEST / 8:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Measuring observables in quantum mechanics is straightforward, and is built into the axiomatics. Measuring how much an observable has changed in a process, however, is notoriously problematic. During the seminar, I will talk about mechanical work and the history of how people tried, and keep trying, to measure it. Aiming to reveal the ultimate source of why no one succeeds in this task, we will take an abstract approach to the problem, by demanding of any work measurement the sheer physical minimum and seeing if those demands can be met at all. We require (A) energy conservation for arbitrary initial states of the system and (B) the main fluctuation theorem for work — the Jarzynski equality — for thermal initial states. By energy conservation we mean that the average work must be equal to the difference of initial and final average energies, and that untouched systems must exchange deterministically zero work. Requirement B encapsulates the second law of thermodynamics and the quantum–classical correspondence principle. We prove that work measurement schemes that do not depend on the system's initial state satisfy B if and only if they coincide with the famous two-point measurement scheme, thereby establishing that state-independent schemes cannot simultaneously satisfy A and B. Expanding to the realm of state-dependent schemes allows for more compatibility between A and B. However, merely requiring the state-dependence to be continuous still effectively excludes the coexistence of A and B, leaving the theoretical possibility open for only a narrow class of exotic schemes.

## 7th IFS Seminar

Title: Efficiency-fidelity trade-off in a quantum error-correcting engine Speaker: Arshag Danageozian, Louisiana State U. Date: Fri 16 July 2021 Time: 9:00 AM CT / 3:00 PM BST / 4:00 PM CEST / 6:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise by preemptively encoding it using an ancillary system. Thermal noise, which plays a central role in quantum thermodynamics (QTD), is a special type of noise due to its presence in almost every implementation of quantum computing and quantum information processing. This suggests a deep link between QEC and QTD which has been discussed previously in the context of Maxwell’s demon. In this article, we view QEC as a quantum heat engine with a feedback controller (demon). The main task of this engine is to correct the effects of the hot bath (thermal noise) by attempting to close the cycle with respect to the system state, corresponding to a perfect QEC. We derive Clausius’ formulation of the 2nd law in the context of this QEC engine operating with general quantum measurements. We show that for low enough temperatures, this leads to a fundamental trade-off between the fidelity of the error-corrected system state and the super-Carnot efficiencies that heat engines with feedback controllers have been known to possess.

## 6th IFS Seminar

Title: An Introduction to Schrödinger Wave Functionals Speaker: Jarah Evslin, Inst. Modern Phys., Lanzhou. Date: Thu 17 June 2021 Time: 9:00 AM PDT / 5:00 PM BST / 6:00 PM CEST / 8:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Each configuration in a quantum field theory corresponds to a map from a space X of functions or bundles with sections to the space of complex numbers. These maps are called Schrödinger wave functionals. They generalize wave functions in quantum mechanics, which are maps from a finite-dimensional manifold to the complex numbers. We review the main properties of wave functions and wave functionals in a series of examples. We describe an embedding of X into this quantum configuration space and argue that perturbative quantum field theory only probes a tubular neighborhood of its image, but that the poorly understood global properties of the quantum configuration space are relevant to the confinement problem in supersymmetric QCD.

## 5th IFS Seminar

Title: Invariant subspaces of elliptic systems Speaker: Matteo Capoferri, Cardiff. Date: Tue 25 May 2021 Time: 10:00 AM PDT / 6:00 PM BST / 7:00 PM CET / 9:00 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$ orthonormal pseudodifferential projections commuting with the operator $A$ and provide an algorithm for the computation of their full symbols, as well as explicit closed formulae for their subprincipal symbols. Pseudodifferential projections yield a decomposition of $L^2(M)$ into invariant subspaces under the action of $A$ modulo $C^\infty(M)$. Furthermore, they allow us to decompose $A$ into $m$ distinct sign definite pseudodifferential operators. We use our pseudodifferential projections to show that the spectrum of $A$ decomposes, up to an error with superpolynomial decay, into $m$ distinct series, each associated with one of the eigenvalues of the principal symbol of $A$. These spectral results are then applied to the study of propagation of singularities in hyperbolic systems. This is joint work with Dmitri Vassiliev (UCL). The talk is based on two recent preprints, arXiv:2103.14325 and arXiv:2103.14334.

## 4th IFS Seminar

Title: Maximum Entropy competes with Maximum Likelihood Speaker: Armen Allahverdyan, YerPhI. Date: Mon 19 April 2021 Time: 11:30 AM PDT / 2:30 PM EDT / 8:30 PM CET / 10:30 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of statistical physics to probabilistic inference. However, a systematic approach towards its validity limits is currently missing. Here we study MAXENT in a Bayesian decision theory set-up, i.e. assuming that there exists a well-defined prior Dirichlet density for unknown probabilities, and that the average Kullback-Leibler (KL) distance can be employed for deciding on the quality and applicability of various estimators. These allow to evaluate the relevance of various MAXENT constraints, check its general applicability, and compare MAXENT with estimators having various degrees of dependence on the prior, viz. the regularized maximum likelihood (ML) and the Bayesian estimators. We show that MAXENT applies in sparse data regimes, but needs specific types of prior information. In particular, MAXENT can outperform the optimally regularized ML provided that there are prior rank correlations between the estimated random quantity and its probabilities.

## 3rd IFS Seminar

Title: Hamiltonian deformations in quantum mechanics Speaker: Edgar Shaghoulian, U Penn. Date: Wed 24 March 2021 Time: 9:30 AM PST / 12:30 PM EST / 5:30 PM CET / 8:30 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: I will present a class of solvable deformations of quantum-mechanical theories. These deformations map the Hamiltonian to a function of itself. We will solve these theories by computing all finite-temperature correlation functions of the deformed theory in terms of the correlators of the undeformed theory. If time permits we will consider applications to statistical systems, disordered systems, and quantum gravity.

## 2nd IFS Seminar

Title: Analog of many-body Berry-Esseen theorem for critical systems Speaker: Karen Hovhannisyan, ICTP (Trieste) Date: Thu 18 February 2021 Time: 9 AM PST / 5 PM GMT / 6 PM CET / 9 PM Yerevan Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: Energetic spectra of many-body systems are impenetrably complex, and very little can be said about them in general. Nonetheless, certain general statements can be made about probability distributions of many-body systems' energies. Most notably, the many-body Berry–Esseen theorem establishes that the energy distribution of a locally interacting quantum lattice Hamiltonian becomes Gaussian in the thermodynamic limit as long as the correlation length is finite. In this talk, I will present a result similar to the Berry–Esseen theorem that extends to lattices with diverging correlation lengths. More specifically, I will show that the energy distribution of a translation-invariant lattice at a finite-temperature phase transition point tends to a Gaussian as long as its specific heat diverges logarithmically in the thermodynamic limit. When the specific heat diverges polynomially, the energy distribution is still unimodal, with exponentially decaying tails, but Gaussianity is no longer guaranteed.

## 1st IFS Seminar

Title: Global hyperbolicity and factorization in cosmological models Speaker: Zhirayr Avetisyan, UC Santa Barbara Date: Tue 8 September 2020 Time: 6 AM GMT / 8 AM CET / 10 AM Yerevan / 2 PM Beijing Delivery mode: Zoom (Contact seminar@ifs.am for the link and password) YouTube Whiteboard PDFAbstract: The subject of the talk is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicty and factorization properties of the spacetime and the vector bundle that are usually independently assumed to hold, are now derived from a minimal set of assumptions based on the recent progress in differential geometry and topology.