Invited Speakers

• Correlation functions of twist fields from hydrodynamics
  Benjamin Doyon, Kings College London
  

  The Euler-scale power-law asymptotics of space-time correlation functions in many-body systems, quantum and classical, can be obtained by projecting the observables onto the hydrodynamic modes admitted by the model and state. This is the Boltzmann-Gibbs principle; it works for integrable and non-integrable models alike. However, certain observables, such as some order parameters in thermal of generalised Gibbs ensembles, do not couple to any hydrodynamic mode: the Boltzmann-Gibbs principle gives zero. I will explain how hydrodynamics can still give the leading exponential decay of order parameter correlation functions. With the examples of the quantum XX chain and the sine-Gordon model, I will explain how large deviations of the spin and U(1) current fluctuations are related to such exponential decay. Exact predictions are given by the ballistic fluctuation theory based on generalised hydrodynamics. In the XX model, this is in agreement with results obtained previously by a more involved Fredholm determinant analysis and other techniques, and even gives a new formula for a parameter regime not hitherto studied. In the sine-Gordon model, these are new results, inaccessible by other techniques. If time permits, I will describe how such ideas also give large-time behaviours of entanglement entropy after quenches. Based on various works in collaborations with Alvise Bastianello, Giuseppe Del Vecchio Del Vecchio, Márton Kormos and Paola Ruggiero.

• Double affine Hecke algebras and integrability of quantized Q-systems
  Rinat Kedem, University of Illinois
  

  The weighted generating functions for the number of solutions to the Bethe equations of generalized Heisenberg spin chains are generalizations of q-Whittaker functions. In some limits, these are related to conformal field theory characters, and have interpretations in enumerative geometry, as well as counting of vacuua in supersymmetric gauge theories. In general, these functions can be constructed via an algebra of raising and lowering operators which is the quantum Q-system, a non-commutative version of the fusion relations for special quantum affine algebra characters. In this talk, I will explain this algebra for the classical affine root systems, and explain its relation to q-Toda equations via Macdonald’s duality.

• Interplay between the planar Gaussian free field, Schramm-Loewner evolutions, and Gaussian multiplicative chaos
  Ellen Powell, Durham University
  

  I will discuss recent advances in the probabilistic approach to building “Liouville quantum gravity surfaces”, based on remarkable couplings between the planar Gaussian free field and a family of random fractal curves known as Schramm-Loewner evolutions. The talk will be based partly on joint works with Juhan Aru, Nina Holden, Avelio Sepulveda, and Xin Sun.

• Gauge theory and Integrable Systems
  Benoit Vicedo, York University
  
  In recent years various unifying frameworks for describing and constructing integrable systems have emerged. In particular, two-dimensional integrable field theories can be constructed either from Gaudin models associated with affine Kac-Moody algebras or from four-dimensional Chern-Simons gauge theory. In this talk I will describe a simplified version of this story whereby finite-dimensional integrable systems can be obtained either from Gaudin models associated with finite-dimensional Lie algebras or from a certain three-dimensional variant of BF theory. I will also explain the connection between the two formalisms, in the finite-dimensional and field theory settings, and review recent progress towards constructing more general integrable field theories from four-dimensional Chern-Simons theory.