Organisers:
Changrim Ahn (Ewha Womans University)
Murray Batchelor (Australia National University)
Anastasia Doikou (Heriot-Watt University)
Patrick Dorey (Durham University)
Paul Pearce (Melbourne University/Queensland University)
Véronique Terras (Paris-Saclay University)

Program Description: 

This research program focusses on the mathematics and physics of integrability in classical/quantum physical systems in 1 and 2 dimensions. Following on from our 2017 MATRIX@Melbourne Research Program, this research program is organised around currently active hot topics and open problems with 50% of the program reserved for group collaboration. The overarching motivation is to muster all the disparate tools pure mathematics has to offer in disciplines such as affine Lie algebras, vertex algebras, planar algebras, quantum algebras and representation theory and apply them to understand, in a deep and precise manner, the behaviour of a diverse range of physical systems arising in disciplines such as classical/quantum statistical mechanics, condensed matter, quantum entanglement/quenches and particle physics. The physical systems of interest include gases and fluids, ferromagnets, ferroelectrics, cold atoms, correlated electron systems, dimers, polymers and percolation among many others.

 Program Topics

• Integrability, symmetries and quantum algebras
• Exactly solvable lattice models
• Bethe ansatz and quantum spin chains
• Diagram algebras, geometric phase transitions and logarithmic CFT
• Bulk and boundary CFT, AdS/CFT, QFT and their perturbations
• Quantum entanglement, quantum quenches and generalised hydrodynamics
• Cold atoms, strongly correlated systems

Program Structure:
  

Talk Title

Week 1 
Murray Batchelor* :Superintegrable chiral Potts, free parafermions and the spin-1 biquadratic model
Chihiro Matsui: A variety of partially solvable models: From closed spin chains to open spin chains
Thomas Quella: Symmetry-protected topological phases with quantum group invariance
Atsuo Kuniba: Solving tetrahedron and 3D reflection equations by quantum cluster algebras
Charlotte Kristjansen: Integrable Monopoles
Rafael Nepomechie 1: Introduction to quantum computing
Junji Suzuki: The dynamical correlation functions of quantum spin chains, revisited
Gabor Takacs: TBA
Francesco Ravanini: Hagedorn singularity in exact U_q(su_2) S-matrix theories with arbitrary spins
Clare Dunning: On rational solutions of the Painlevé equations
Marton Kormos: Thermodynamics, transport, and fluctuations in the sine-Gordon model
Roberto Tateo 1: TTbar deformations and integrable models

Week 2
Andreas Klümper 1: Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
Rafael Nepomechie 2: Quantum state preparation: Dicke and Bethe states
Changrim Ahn: UV Complete QFTs by TTbar deformations
Roberto Tateo 2: Interconnections between TTbar-like flows, nonlinear electrodynamics, and modified gravity theories
David Ridout 1: Reducible but indecomposable: representation theory for 21st century mathematical physics
Zoltan Bajnok: Resurgence in integrable models
Didina Serban 1: Integrable long range spin chains with extended symmetry
David Ridout 2: Representations of fractional-level WZW models and W-algebras
Francisco Alcaraz: Conformally invariant free parafermion quantum chains with multispin interactions
Didina Serban 2: Correlation functions in integrable supersymmetric four dimensional gauge theories
Véronique Terras: On correlation functions of the open XXZ and XYZ spin chains with boundary fields related by a constraint
Paul Pearce: Modular covariant torus partition function of dense and dilute loop models
Patrick Dorey: TBA
Anastasia Doikou: Set-theoretic Yang-Baxter equation: quantum algebras & universal R-matrices
Xiwen Guan: New results in 1D repulsive Hubbard model: Quantum liquid, criticality and transport

Week 3
Angela Foerster: Integrability in the design and control of quantum devices
Jon Links: Yang-Baxter with bosons: from cold atoms to the failure of an exact solution
Robert Weston: New Results on Factorization of Cyclic Representations of U_q(hat{sl}_2), with Applications to the Chiral-Potts Model
Wen-Li Yang: Off-diagonal approach to the exact solution of quantum integrable systems
Jean-Emile Bourgine: A Calogero model for the non-Abelian quantum Hall effect
Andreas Klümper 2: Chiral Basis for Qubits and Spin-Helix Decay
Junpeng Cao: Exact solution of quantum integrable systems without U(1) symmetry
Ana Retore: Two elliptic integrable deformations of AdS3 x S3 S-matrix
William Mead TBA
Alexandr Garbali TBA
Remy Adderton TBA
Jan de Gier TBA

Confirmed International Participants: 
Organisers:
Changrim Ahn^ (Ewha Womans University, Seoul, South Korea)
Anastasia Doikou‡ (Heriot-Watt University, Edinburgh, Scotland)
Patrick Dorey‡ (Durham University, England)
Véronique Terras‡ (Paris-Saclay University, France)

Keynote speakers:
Andreas Klümper‡ (Bergische University, Wuppertal, Germany)
Rafael Nepomechie‡ (Miami University, Florida, USA)
Didina Serban*† (CEA Saclay, France)
Roberto Tateo† (INFN, Torino University, Italy)

Key Participants:
Francisco Alcaraz‡ (Sao Paulo University, Sao Carlos, Brazil)
Zoltan Bajnok (Wigner Research Centre for Physics, Budapest, Hungary)
Junpeng Cao (IOP, CAS, China)
Clare Dunning (University of Kent, Kent, England)
Angela Foerster (UFRGS, Porto Alegre, Brazil)
Xiwen Guan (WIPM, Wuhan, China)
Marton Kormos (BUTE, Budapest, Hungary)
Charlotte Kristjansen (Niels Bohr Institute, Denmark)
Atsuo Kuniba^ (Tokyo University, Tokyo, Japan)
Chihiro Matsui^ (Tokyo University, Tokyo, Japan)
Francesco Ravanini (Bologna University, Bologna, Italy)
Ana Retore (Durham University, Durham, England)
Junji Suzuki^ (Shizuoka University, Shizuoka, Japan)
Gabor Takacs (BUTE, Budapest, Hungary)
Wen-Li Yang^ (Northwest University, Xian, China)
Robert Weston (Heriot-Watt University, Edinburgh, Scotland)

Confirmed Australian Participants:
Organisers:
Murray Batchelor (ANU, Canberra, Australia)
Paul Pearce (Melbourne University/UQ, Australia)

Keynote Speakers:
David Ridout† (Melbourne University, Australia)

Key Participants:
Jean-Emile Bourgine (Melbourne University, Australia)
Peter Bouwknegt (ANU, Canberra, Australia)
Jan de Gier (Melbourne University, Australia)
Jon Links (UQ, Brisbane, Australia)
Thomas Quella (Melbourne University, Australia)
William Mead (University of Melbourne)
Alexandr Garbali (University of Melbourne)
Remy Adderton (Australian National University)

†: AMSI
*: SMRI
^: APCTP
‡: Simons
Registration:

• Registration is now closed
• Arrival Date: 1 July 2024
• Departure Date: 19 July 2024

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 4 July 2024
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.

This MATRIX Research Program benefits from the sponsorship of