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Monday, 16 July 2018
Time Speaker Title Resources
09:30 to 10:45 -- Welcome by Prof.Spenta Wadia
10:00 to 11:00 Thomas Trogdon The computational theory of Riemann–Hilbert problems (Lecture 1)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 David Smith The Unified Transform Method for linear evolution equations (Lecture 1)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Venky Krishnan An inverse problem for the relativistic Schrödinger equation with partial boundary data

We study the inverse problem of determining vector and scalar potentials appearing in the relativistic Schrödinger equation in space dimension 3 or higher from information about the solution on a suitable subset of the boundary. We prove unique determination of these potentials modulo a natural gauge invariance. This is joint work with Manmohan Vashisth.

15:30 to 17:00 -- Discussions / Research
Tuesday, 17 July 2018
Time Speaker Title Resources
10:00 to 11:00 Thomas Trogdon The computational theory of Riemann–Hilbert problems (Lecture 2)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 David Smith The Unified Transform Method for linear evolution equations (Lecture 2)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Chitrabhanu Chaudhuri Intersection Theory on Moduli Space of Curves and their connection to Integrable Systems

We shall talk about the Witten conjecture which roughly says that the generating function of certain intersection numbers on the moduli space of curves satisfies the KdV equation. We shall also discuss a proof of the celebrated conjecture using the ESLV formula which relates them to Hurwitz numbers. Surprisingly the generating function for Hurwitz numbers satisfies the KP hierarchy.

15:30 to 17:00 -- Discussions / Research
Wednesday, 18 July 2018
Time Speaker Title Resources
10:00 to 11:00 Thomas Trogdon The computational theory of Riemann–Hilbert problems (Lecture 3)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 David Smith The Unified Transform Method for linear evolution equations (Lecture 3)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Alexander Bobenko CMC Surfaces (classical and discrete) and their Relation to Integrable Systems (Lecture 1)
15:30 to 17:00 -- Discussions / Research
18:00 to 19:30 -- Cultural program
Thursday, 19 July 2018
Time Speaker Title Resources
10:00 to 11:00 Thomas Trogdon The computational theory of Riemann–Hilbert problems (Lecture 4)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 David Smith The Unified Transform Method for linear evolution equations (Lecture 4)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Alexander Bobenko CMC Surfaces (classical and discrete) and their Relation to Integrable Systems (Lecture 2)
15:30 to 17:00 -- Discussions / Research
Friday, 20 July 2018
Time Speaker Title Resources
10:00 to 11:00 Alexander Bobenko CMC Surfaces (classical and discrete) and their Relation to Integrable Systems (Lecture 3)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Mythily Ramaswamy Control of fluid motion

After introducing controllability (reaching a desired state in finite time) and stabilizability (reaching a steady state as time tends to infinity), for ODE systems, I will discuss these  issues for some PDE systems, arising in fluid models.

12:30 to 14:00 -- Lunch
14:30 to 15:30 Alexander Bobenko CMC Surfaces (classical and discrete) and their Relation to Integrable Systems (Lecture 4)
16:00 to 17:30 Eldad Bettelheim Integrability in the Laplacian Growth Problem

Laplacian growth is a problem of two-dimensional pattern formation, that has drawn a lot of attention in theoretical and experimental physics due to the spontaneous formation of fractal patterns in a non-equilibri um system. Although the problem has been shown to be integrable, albeit it in a somewhat unexpected and unconventional way, an explanation of the fractal properties of the growth has eluded theoretical study. Attempting to be methodical, I will first review the problem and its relation to integrable systems, then I will undoubtedly add to the confusion by suggesting tentative and speculative directions of research.

Monday, 23 July 2018
Time Speaker Title Resources
10:00 to 11:00 Amit Apte TBA
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Ritwik Mukherjee Quantum Cohomology and WDVV equation (Lecture 1)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Varun Thakre TBA
15:30 to 16:00 -- Tea/Coffee
16:00 to 17:30 -- Discussions / Research
Tuesday, 24 July 2018
Time Speaker Title Resources
10:00 to 11:00 Nuno Romao The Nahm-Schmid equations: integrability and hypersymplectic geometry
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Ritwik Mukherjee Quantum Cohomology and WDVV equation (Lecture 2)
12:30 to 14:00 -- Lunch
14:30 to 15:30 Kaushal Verma Non-autonomous basins of attraction

This will be an elementary introduction to Fatou-Bieberbach domains and Short C^k's.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:30 -- Discussions / Research
Wednesday, 25 July 2018
Time Speaker Title Resources
10:00 to 11:00 Vishal Vasan Fractional derivatives, boundary-value problems and the motion of inertial particles in a viscous fluid

Fractional derivatives are as old integer derivatives and yet they have no unique definition. In this talk, I'll introduce a new perspective on fractional derivatives highlighting their connection to boundary-value problems for partial differential equations. This perspective readily affords a general framework to analyse fractional differential equations. The motivating physical problem is that of a small heavy particle in a viscous fluid. The upshot of our analysis is a much simpler proof for existence of solutions to such equations as well as a new numerical method to compute solutions in an efficient and accurate manner.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Joseph Samuel Some Integrable Models and Supersymmetry

I will describe three models of physical interest in which Integrability and Supersymmetry are entwined. We will start with two elementary examples and end with a model which is still a topic of current research.

12:30 to 14:00 -- Lunch
14:30 to 15:30 Arvind Ayyer Alternating Sign Triangles

We present results on a combinatorial problem which was solved recently using techniques from integrable systems. Specifically, we introduce a new class of square-ice configurations (also known as six-vertex model configurations) on triangular subsets of the square lattice, which we call Alternating Sign Triangles (ASTs). The proof of the enumeration of ASTs uses the integrability of the six-vertex (or square-ice) model. We will explain the origin of this problem and the ideas involved in the proof. Time permitting, we will also give product formulas for other classes of square-ice configurations using similar ideas. This is joint work with Ilse Fischer and Roger Behrend.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:30 Paul Wiegmann Hofstadter problem: Integrability and Complexity (Lecture 1)
Thursday, 26 July 2018
Time Speaker Title Resources
10:00 to 11:00 Robert Buckingham Painleve Equations

The six Painleve equations are second-order ordinary differential equations whose solutions serve as nonlinear special functions for many problems in mathematical physics.  We will give an overview of various applications of Painleve functions to integrable probability and nonlinear wave equations, and then discuss their integrable structure and asymptotic analysis.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Vasudeva Murthy Forced integrable systems: the case of sine-Gordon equation

The sine-Gordon equation is a semi-linear wave equation used to model many physical phenomenon like seismic events that includes earthquakes, slow slip and after-slip processes, dislocation in solids etc. Solution of homogeneous sine- Gordon equation exhibit soliton like structure that propagates without change in its shape and structure. The question whether solution of sine- Gordon equation still exhibit soliton like behaviour under an external forcing has been challenging as it is extremely difficult to obtain an exact solution even under simple forcing like constant. In this study solution to an inhomogeneous sine-Gordon equation with Heaviside forcing function is analysed. Various one- dimensional test cases like kink and breather with no flux and non reflecting boundary conditions are studied.

12:30 to 14:00 -- Lunch
14:30 to 16:00 Paul Wiegmann Hofstadter problem: Integrability and Complexity (Lecture 2)
15:30 to 16:00 -- Tea/Coffee
16:00 to 17:30 -- Discussions / Research
Friday, 27 July 2018
Time Speaker Title Resources
10:00 to 11:00 Subhojoy Gupta Quadratic differentials and measured foliations on Riemann surfaces

Let S be a closed oriented surface of genus at least two. The Teichmüller space T(S) is the universal cover of the moduli space of hyperbolic structures on S. For any choice of a complex structure on S, a theorem of M. Wolf, and independently N. Hitchin, identifies T(S) with the vector space of holomorphic quadratic differentials on the resulting Riemann surface X, that we denote by Q(X). An earlier result of Hubbard and Masur identifies Q(X) with the space of certain topological objects called measured foliations on S. I shall discuss these results, the relation between them, and their generalizations to the case of meromorphic quadratic differentials. All these spaces have some natural symplectic structures, and I shall mention some open questions concerning them.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Rukmini Dey Geometric quantization of finite Toda systems and coherent states

We shall first talk about Kostant-Souriau's method of geometric quantization of coadjoint orbits. Adler had showed that the Toda system can be given a coadjoint orbit description. We shall talk about quantization of the Toda system by viewing it as a single orbit of a multiplicative group of lower triangular matrices of determinant one with positive diagonal entries. We get a unitary representation of the group with square integrable polarized sections of the quantization as the module . We find the Rawnsley coherent states after completion of the above space of sections. Finally we give an expression for the quantum Hamiltonian for the system.This is joint work with Dr. Saibal Ganguli.

12:30 to 14:00 -- Lunch
16:00 to 17:30 -- Discussions / Research
Monday, 30 July 2018
Time Speaker Title Resources
09:30 to 11:00 Alexander Abanov Hydrodynamics, variational principles and integrability (Pedagogical Lecture 1)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Sergei Lukyanov Exact instanton summation in O(3) non-linear sigma model

Bukhvostov and Lipatov showed that weakly interacting instantons and anti-instantons in the O(3) NLSM in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. The model can be reformulated as a bosonic QFT with two interacting bosons, which upon an analytic continuation into a strong coupling regime, become equivalent to the originating O(3) NLSM. This observation provides a remarkable opportunity for the exact instanton counting. As an illustration, I will discuss the calculation of the vacuum energy of the O(3) NLSM with twisted boundary conditions.

12:30 to 14:00 -- Lunch
14:00 to 15:30 Joel Moore Dynamics and transport in integrable and nearly integrable models (Lecture 1)

These talks review various approaches to non-equilibrium processes in integrable models. Examples include the increase in understanding since 2011 of Drude weight and semiclassical kinetic theory in integrable models, and obtaining exact far-from-equilibrium results for some quantities in the XXZ model through expansion potentials. In many cases the predictions of theoretical approaches based on integrability can be confirmed due to progress in DMRG and other matrix product state algorithms, and the essentials of such algorithms will be reviewed.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Giuseppe Mussardo The Generalised Riemann Hypothesis (Special Colloquium)
Tuesday, 31 July 2018
Time Speaker Title Resources
09:30 to 11:00 Alexander Abanov Hydrodynamics, variational principles and integrability (Pedagogical Lecture 2)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Nuno Romao Statistical physics of 2d gas mixtures from symplectic volumes of vortex moduli
12:30 to 14:00 -- Lunch
14:00 to 15:30 Joel Moore Dynamics and transport in integrable and nearly integrable models (Lecture 2)

These talks review various approaches to non-equilibrium processes in integrable models. Examples include the increase in understanding since 2011 of Drude weight and semiclassical kinetic theory in integrable models, and obtaining exact far-from-equilibrium results for some quantities in the XXZ model through expansion potentials. In many cases the predictions of theoretical approaches based on integrability can be confirmed due to progress in DMRG and other matrix product state algorithms, and the essentials of such algorithms will be reviewed.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Kareljan Schoutens Many-body strategies for multi-qubit gates

The standard method for implementing algorithms for quantum computation is through quantum circuits. Such circuits typically contain quantum gates involving more than a single or two qubits. Multi-qubit gates can be decomposed into 1- and 2-qubit gates, but this is not necessarily the most efficient strategy. We present a framework for quantum control directly at the level of multiple qubits. A key ingredient is what we call an eigengate: a simple quantum circuit that maps computational basis states to eigenstates of a many-body hamiltonian. We show how to make it all work for a Krawtchouk qubit chain, and for operators associated to a spin chain with inverse square exchange, first introduced by Polychronakos. 
Based on arXiv:1707.05144, Phys Rev A97.04232, with Koen Groenland

Wednesday, 01 August 2018
Time Speaker Title Resources
09:30 to 11:00 Alexander Abanov Hydrodynamics, variational principles and integrability (Pedagogical Lecture 3)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Giuseppe Mussardo Yang-Lee Zeros in Integrable Quantum Field Theories

We address the Yang-Lee formalism for Integrable Quantum Field Theories, discussing various features of this approach to statistical physics and focusing the attention on the zeros of the grand canonical partition in the fugacity variable of the soliton sector of the Sine-Gordon model and of the simplest integrable quantum field theory, the so called Yang-Lee model.

12:30 to 14:00 -- Lunch
14:00 to 15:30 Joel Moore Dynamics and transport in integrable and nearly integrable models (Lecture 3)

These talks review various approaches to non-equilibrium processes in integrable models. Examples include the increase in understanding since 2011 of Drude weight and semiclassical kinetic theory in integrable models, and obtaining exact far-from-equilibrium results for some quantities in the XXZ model through expansion potentials. In many cases the predictions of theoretical approaches based on integrability can be confirmed due to progress in DMRG and other matrix product state algorithms, and the essentials of such algorithms will be reviewed.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 -- Discussions / Research
Thursday, 02 August 2018
Time Speaker Title Resources
09:30 to 11:00 Alexios Polychronakos Physics and Mathematics of Quantum and Classical Calogero models (Lecture 1)

A review of the Calogero integrable model and its various generalizations will be given, with emphasis on physical properties and recent results. Topics will include integrability, the connection of these systems with fractional statistics, their matrix model and operator formulations, their various reductions and extensions, and their hydrodynamic description, properties and solitons.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Kirone Mallick Exact solution for single-file diffusion

A particle in a one-dimensional channel with excluded volume interaction displays anomalous diffusion with fluctuations scaling at t1/4, in the long-time limit. This phenomenon, seen in various experimental situations, is called single-file diffusion. In this talk, we shall present the exact formula for the distribution of a tracer and its large deviations in the one-dimensional symmetric simple exclusion process, a pristine model for single-file diffusion, thus answering a problem that has eluded solution for decades. We use the mathematical arsenal of integrable probabilities developed recently to solve the one-dimensional Kardar-Parisi-Zhang equation. Our results can be extended to situations where the system is far from equilibrium, leading to a Gallavotti-Cohen Fluctuation Relation and providing us with a highly nontrivial check of the Macroscopic Fluctuation Theory. 

Joint work with Takashi Imamura (Chiba) and Tomohiro Sasamoto (Tokyo).

12:30 to 14:00 -- Lunch
14:30 to 15:30 Kareljan Schoutens Supersymmetric lattice models

Lattice models for itinerant (spin-less) fermions can be tuned to display supersymmetry (susy): a fermionic symmetry that squares to the hamiltonian time evolution. Critical and massive phases of the susy Mk models on 1D lattices are described by minimal models of superconformal field theory or by (integrable) massive QFT. Many susy lattice models, including Nicolai and susy SYK models in 1D and the susy M1 model on 2D lattices) feature extensive degeneracies of supersymmetric ground states. We discuss how such ground states can be counted and explore the implications of their existence. We also present topological pumping protocols of 2-particle bound states that are protected by supersymmetry. Includes recent results obtained with Sergey Shadrin, Ruben La, and Bart van Voorden

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Krishnendu Sengupta Quantum dynamics with stochastic reset

We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat O$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.

Friday, 03 August 2018
Time Speaker Title Resources
09:30 to 11:00 Alexios Polychronakos Physics and Mathematics of Quantum and Classical Calogero models (Lecture 2)

A review of the Calogero integrable model and its various generalizations will be given, with emphasis on physical properties and recent results. Topics will include integrability, the connection of these systems with fractional statistics, their matrix model and operator formulations, their various reductions and extensions, and their hydrodynamic description, properties and solitons.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Emil Yuzbashyan Integrable time-dependent Hamiltonians and Knizhnik-Zamolodchikov equations

I will outline a way to make the parameters (e.g., the interaction strength) of certain quantum integrable models time-dependent without breaking their integrability. Interesting many-body models that emerge from this approach include a superconductor with the interaction strength inversely proportional to time, a Floquet BCS superconductor, and the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance as well as various models of multi-level Landau-Zener tunneling.

Amazingly, the non-stationary Schrodinger equation for all these models has a similar structure and is integrable with a similar technique as the famous Knizhnikov-Zamolodchikov equations of the Conformal Field Theory. I will use this to solve for their dynamics and also discuss some interesting physics that emerges at large times.

12:30 to 14:00 -- Lunch
14:30 to 15:30 Hosho Katsura Sine-square deformation of one-dimensional critical systems

Sine-square deformation (SSD) is one example of smooth boundary conditions that have significantly smaller finite-size effects than open boundary conditions. In a one-dimensional system with SSD, the interaction strength varies smoothly from the center to the edges according to the sine-square function. Thus, the Hamiltonian of the system lacks translational symmetry. Nevertheless, previous studies have revealed that the SSD leaves the ground state of the uniform chain with periodic boundary conditions (PBC) almost unchanged for critical systems. In particular, I showed that the correspondence is exact for critical XY and quantum Ising chains. The same correspondence between SSD and PBC holds for Dirac fermions in 1+1 dimension and a family of more general conformal field theories. If time permits, I will also review more recent results and discuss the excited states of the SSD systems. 

[1] H. Katsura, J. Phys. A: Math. Theor. 44, 252001 (2011); 45, 115003 (2012).
[2] I. Maruyama, H. Katsura, T. Hikihara, Phys. Rev. B 84, 165132 (2011)."

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Giuseppe Mussardo Movie on Chandrasekhar
Monday, 06 August 2018
Time Speaker Title Resources
09:30 to 11:00 Alexios Polychronakos Physics and Mathematics of Quantum and Classical Calogero models (Lecture 3)

A review of the Calogero integrable model and its various generalizations will be given, with emphasis on physical properties and recent results. Topics will include integrability, the connection of these systems with fractional statistics, their matrix model and operator formulations, their various reductions and extensions, and their hydrodynamic description, properties and solitons.

11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Manas Kulkarni Integrability with confined potentials: Duality, Solitons, Field Theory and Growth of Perturbations
12:30 to 14:00 -- lunch
14:30 to 15:30 Gautam Mandal Some results on thermalization in integrable models
15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Takeshi Morita Bound on chaos and acoustic Hawking radiation in free fermi fluid

Recently the upper bound on the Lyapunov exponent in thermal quantum systems was conjectured by Maldacena, Shenker and Stanford. I investigate this bound in a semi-classical dynamical system and argue the implication of this bound. Particularly I will show that this bound is related to a spontaneous energy emission in quantum mechanics. As an example, acoustic Hawking radiation in free fermi fluid will be explained through this energy emission.

Tuesday, 07 August 2018
Time Speaker Title Resources
09:30 to 11:00 Fabian Essler Integrability out of equilibrium (Lecture 1)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Fabio Franchini The Frustration in being Odd: area law violation in local systems.

"We consider anti-ferromagnetic spin chains with a weak frustration -just one bond in a large chain-, such as systems with an odd number of spins with periodic boundary conditions. We show that, in certain cases, a new quantum phase of matter arises in these systems. Such phase is extended, gapless, but not relativistic. The low-energy excitations have a quadratic (Galilean) spectrum. Locally, the correlation functions on the ground state do not show significant deviations compared to the not-frustrated case, but correlators involving a number of sites (or distances) scaling like the system size display new behaviors. In particular, the Von Neumann entanglement entropy is found to follow new rules, for which neither area law applies, nor one has a divergence of the entropy with the system size. Such very long range correlations are novel and of potential technological interest. We display such new phase in a few prototypical chains using numerical simulations and we study analytically the paradigmatic example of the Ising chain. Through these examples we argue that this phase emerges generally in (weakly) frustrated systems with discrete symmetries.

[1] S.M. Giampaolo, F. Ramos, and F. Franchini, In Preparation"

12:30 to 14:00 -- Lunch
14:30 to 15:30 Abhishek Dhar Two-point correlations and classical analogues of the "Out-of-Time-Ordered-Commutator"

The talk will discuss the form of standard two-point equilibrium spatio-temporal correlations of observables in classical integrable systems such as the Toda chain. Next we will discuss the form of the classical analogue of the Out-of-Time-Ordered-Commutator [OTOC] in such systems.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Alexios Polychronakos 100 Years of Feynman - and 30 without him: some reminiscences

The correspondence between the one-dimensional Calogero model and the two-dimensional lowest Landau level anyon model is known for some time, but the mapping between the models was so far rather formal. I will present an explicit mapping between the N-body harmonic Calogero eigenstates to the lowest Landau level eigenstates of N anyons in a harmonic trap. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation.

Wednesday, 08 August 2018
Time Speaker Title Resources
09:30 to 11:00 Fabian Essler Integrability out of equilibrium (Lecture 2)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Alexios Polychronakos Mapping the Calogero model to the anyon model

A review of the Calogero integrable model and its various generalizations will be given, with emphasis on physical properties and recent results. Topics will include integrability, the connection of these systems with fractional statistics, their matrix model and operator formulations, their various reductions and extensions, and their hydrodynamic description, properties and solitons.

12:30 to 14:00 -- Lunch
14:30 to 15:30 Sriram Ganeshan Odd surface waves in two-dimensional incompressible fluids

In everyday fluids, the viscosity is the measure of resistance to the fluid flow and has a dissipative character. Avron, Seiler, and Zograf showed that viscosity of a quantum Hall (QH) fluid at zero temperature is non-dissipative. This non-dissipative viscosity (also known as ‘odd’ or ‘Hall’ viscosity) is the antisymmetric component of the total viscosity tensor and can be non-zero for parity violating fluids. I will discuss free surface dynamics of a two-dimensional incompressible fluid with the odd viscosity (not quite quantum Hall hydro). For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral. In the limit of vanishing shear viscosity and gravity, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. In a small surface angle approximation, the equation of motion results in a new class of non-linear chiral dynamics which we dub as {\it chiral Burgers} equation. I will briefly discuss how this program can be extended to the free surface of quantum Hall hydrodynamics.

15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Alexios Polychronakos The 2017 Nobel Prize in Physics -- Gravitational Waves
Thursday, 09 August 2018
Time Speaker Title Resources
09:30 to 11:00 Fabian Essler Integrability out of equilibrium (Lecture 3)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Masahito Yamazaki Integrability from Four-Dimensional Chern-Simons Theory

I will describe new approach to integrable models from the “four-dimensional Chern-Simons theory”, in collaboration with Kevin Costello and Edward Witten. This can be thought of as an analog of the Witten’s explanation of the knot invariants via the three-dimensional Chern-Simons theory. It would be interesting to put our work in broader context of statistical physics and condensed matter physics.

12:30 to 14:00 -- Lunch
14:00 to 15:30 Fabio Franchini Basic Lectures on Bethe Ansatz (Pedagogical Lecture 1)
15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Fabian Essler TBA
Friday, 10 August 2018
Time Speaker Title Resources
09:30 to 11:00 Fabio Franchini Basic Lectures on Bethe Ansatz (Pedagogical Lecture 2)
11:00 to 11:30 -- Tea/Coffee
11:30 to 12:30 Sumilan Banerjee On the stability of many-body localization in d > 1

I will talk about the potential instability of many-body localized systems in the presence of an ‘ergodic bubble’, a finite but large delocalized region within an insulator. I will discuss some recent arguments suggesting that for two and higher dimensions a localized system is unstable even in the presence of a single ergodic bubble. To examine these arguments, we construct several models of a finite ergodic bubble coupled to an Anderson insulator of non-interacting fermions. We first describe the ergodic region using a GOE random matrix and perform an exact diagonalization study of small systems. I will show that the results are in excellent agreement with a refined theory of the thermalization, lending strong support to the avalanche scenario. I will then talk about the limit of large system sizes by modeling the ergodic region via a Hubbard model with all-to-all random hopping. The combined system, consisting of the bubble and the insulator, can be reduced to an effective Anderson impurity problem. We find that the spectral function of a local operator in the ergodic region changes dramatically when coupled to a large number of Anderson fermions, suggesting a possible way in which the instability argument can fail.

12:30 to 14:00 -- Lunch
14:00 to 15:30 Fabio Franchini Basic Lectures on Bethe Ansatz (Pedagogical Lecture 3)
15:30 to 16:00 -- Tea/Coffee
16:00 to 17:00 Alexander Abanov What is common between falling cats and quantum Hall effect? (Public talk)