Hamiltonian Structure of Rational Isomonodromic Deformation Systems and Mathematical Physics

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Explore advanced topics in mathematical physics through this comprehensive 3-day conference featuring expert presentations on cutting-edge research. Delve into Hamiltonian structures, isomonodromic deformation systems, and quantum field theories through lectures covering rational isomonodromic deformations, finite-dimensional Lie algebras of Hamiltonian vectors, and quasinormal modes. Examine quantum many-body systems including fermionic symmetry-enriched phases, higher-dimensional quantum Hall effects, and quantum spin chains with their entanglement properties. Investigate integrable systems through discussions of CKP hierarchy, Lagrangian Grassmannians, Bethe ansatz methods, and their applications to quantum computing. Study algebraic structures including centralizer algebras, SU(3) representations, moduli spaces of principal bundles, and categorification techniques. Analyze spectral theory concepts such as transalgebraic spectral curves, quantum curves, and Hurwitz numbers alongside fractal symmetries and phase transitions. Explore soliton dynamics, nonlinear bosonization of Fermi liquids, and quantum Floquet dynamics leading to integrable vertex models. Discover quantum information applications through symmetry-resolved entanglement measures, quantum cryptography with untrusted devices, and quantum renormalization group methods. Examine mathematical structures including Heun equations, conformal blocks, Newton polygons, and sine-Gordon reductions in higher dimensions. Investigate advanced topics in quantum gravity, celestial holography, twistors, and the Siegel-Weil formula as quantum gravity averages. Study hydrodynamics of integrable systems, critical quantum spin liquids, and Gross-Neveu theories describing phase transitions. Analyze mathematical tools including Airy kernel determinants, KdV equations, Poisson geometry of noncommutative cluster algebras, and tau functions with their WKB expansions. Explore correlation functions for unitary invariant ensembles, monopole operators in quantum electrodynamics, and coherent states for rational extensions of quantum systems.

Syllabus

John Harnad: Hamiltonian structure of rational isomonodromic deformation systems
Javier de Lucas Araujo: The classification of finite-dimensional Lie algebras of Hamiltonian vector.
Juliàn Barragan Amado: Quasinormal modes via isomonodromy
David Aasen: Characterization and classification of Fermionic Symmetry enriched phases
Dimitra Karabali: Aspects of higher dimensional quantum Hall: effective actions entanglement entropy
Loïc Poulain d'Andecy: Uses of centralizer algebras and the missing label of SU(3)
Emily Cliff: Moduli spaces of principal 2-group bundles& categorificationof Freed-Quinn line bundle
Andrzej Pokraka: The duals of Feynman Integrals
Semeon Artamonov: CKP hierachy and infinite dimensional Lagrangian Grassmannian
Rafael Nepomechie: Bethe ansatz and quantum computing
Vincent Bouchard: Transalgebraic Spectral Curves, Quantum Curves, and Atlantes Hurwitz Numbers
Cenke Xu: Phases and Phase Transitions with Fractal Symmetries: Models and Experimental Platform
Nicolas Crampe: Absorption or Emission of Solitons
Luca Delacretaz: Nonlinear Bosonization of Fermi Liquids
Paul Terwilliger: The alternating central extension of the $q$-Onsager algebra
Yuan Miao: Floquet Baxterisation: from quantum Floquet dynamics to integrable vertex models
Gilles Parez:Symmetry-resolved entanglement measures in quantum many-body systems out of equilibrium
Frédéric Dupont-Dupuis: Quantum Cryptography with untrusted devices
Accessory parameters in Heun equations and classical conformal blocks
Integrable systems from a Newton Polygon
Réductions d'une équation de sine-Gordon en 2+1 dimensions
Isomonodrtomy aspects of the tt* equations of Cecotti and Vafa. Iwasawa factorization & asymptotics
Some intuition and some asymptotic analysis: from two solitons to a continuum limit of solitons
Celestial holography and twistors
Quantum Renormalization Group
Excitations and ergodicity of critical quantum spin chains from non-equilibrium classical dynamics
q-Opers, QQ-systems and Bethe Ansatz
The Siegel-Weil Formula and Quantum Gravity as an Average
The hydrodynamics of many-body integrable systems
Critical properties of quantum spin liquid phase transitions described by ... Gross-Neveu theories
Momenta spacing distributions in anharmonic oscillators
Airy kernel determinants, the KdV equation, and conditional point processes
Poisson Geometry of Noncommutative Cluster Algebras
Generating function of monodromy symplectomorphism, isomonodromic tau-function and its WKB expansion
Tau functions as Widom constants
Correlation functions for unitary invariant ensembles and Hurwitz numbers
Monopole operators in Quantum Electrodynamics
Opérateurs d'échelle et états cohérents pour des extensions rationnelles du système de Rosen-Morse
Polynomial tau-functions of the KP and BKP bilinear identities
Isomonodromic tau functions on Riemann Surfaces through free fermions and four-dimensional QFTs
Polynomial solutions of KP and Gelfand-Dickey hierarchies
Non-linear ladder operators and coherent states for the 2:1 oscillator
Anharmonic oscillator: a solution
Hilbert Space Fragmentation
Fermionic limit shapes
Bulk and boundary entanglement entropy in the quantum Hall effect: exact results
Duality functions for interacting particle processes and orthogonal polynomials
Integrable quantum spin chains with free fermionic and parafermionic spectrum
Asymptotics of the averaged characteristic polynomial for Ginibre Ensemble
New infinite families of Nth-order superintegrable systems
Sklyanin algebras, Askey-Wilson polynomials and Heun operators
Embedding of Racah algebra and superintegrable systems
Signal analysis and quantum formalism: Quantizations with no Planck constant
Fermionic approach to bilinear expansions of KP correlators in terms of BKP correlators
General solution of the exceptional Hermite differential equation and more
The geometry and physics of Hitchin systems
Fourth Painlevé and Ermakov equations: quantum invariants and more
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