Organisers:
Victor Fagundes (La Trobe University)
Siyu Li (La Trobe University)
Anthony Parr (The University of Queensland)
Yuyang Zhou (The University of Melbourne)
Junze Zhang (The University of Queensland)

Description: This symposium explores integrable and non-commutative integrable Hamiltonian systems from both geometric and algebraic perspectives, highlighting their influence in areas such as Poisson and symplectic geometry, quantum dynamics, and various branches of physics. It focuses on the algebraic and geometric structures underlying Hamiltonian dynamics, their role in constructing (super)integrable systems, and their importance for conserved quantities, integrability conditions, and quantisation. It will gather participants who are interested in constructing of the (super-)integrable Hamiltonian systems in geometric respect, and their applications in different aspects from mathematical physics to exchange ideas and solve open problems.

This symposium will provide a platform for participants to discuss and collaborate, to promote communication between students and senior lecturers, as well as, to promote potential international discussions and collaborations.

Topics:
• Geometric and Algebraic Constructions: Detailed exploration of finding integral of motions, Hamiltonians for integrable and superintegrable models via momentum maps on phase
spaces, e.g. homogeneous spaces, symmetric algebras, which are essential for determining the Poisson algebras and foliation in the corresponding Poisson manifolds.
• Algebraic Techniques: Representation theory of Poisson polynomial algebras for explicitly calculating energy spectrum of Hamiltonians.
• Exactly (ES) and Quasi-Exactly Solvable (QES) Systems: Analysis illuminating spectrum properties and exact solutions of QES system via functional Bethe Ansatz method analytically
and numerically, studying deformed Hamiltonian and extending family of QES potential by supersymmetry quantum mechanics, and exploring algebraic structures of the ODE transformed
from Hamiltonian.
• Yang-Baxter Integrability: Yang-Baxter equation (YBE) ensures the factorization of scattering processes in integrable systems. It plays a fundamental role in the quantum inverse scattering
method (QISM) and the theory of exactly solvable models.
• Applications in Mathematical Physics: Direct implications for Bethe Ansatz solutions, quantum many-body problems, related to many aspects of physics, such as superconductivity,
quantum optics, atomic physics, etc.

Through this focused approach, the event enhances theoretical understanding, promotes deeper physical insights, and links abstract mathematical concepts to concrete applications.

Contact:
For queries about the symposium, please contact Siyu Li at Siyu.Li@latrobe.edu.au

keynote Speakers:
(1) Dr. Shizhuo Yu (Nankai University)
(2) Prof. Chuan-Zhong Li (Shandong University of Science and Technology, China)
(3) Dr. Ian Marquette (La Trobe University)
(4) Dr Peter Van Der Kamp (La Trobe University)
(5) A/Prof. Jon Links (The University of Queensland)
(6) Prof. Wen-Li Yang (Northwest University, China)

Speakers:
Dr. Veronica Pasquarella (SIMIS, China)
Kyan Nguyen (La Trobe University, Australia)
He (Oliver) Lyu (Nankai University, China)
Dr. Guorui Ma (Tsinghua University, China)
Dr. Kai Jiang (Beijing university of chemical technology, China)
Dr. Yasushi Ikeda (Cracow University of Technology, Poland)
Mikhail Vasilev (The University of Glasgow, UK)
Victor Fagundes (La Trobe University, Australia)
Samuel Jimenez-Swain (The University of Queensland, Australia)
Anthony Parr (The University of Queensland, Australia)
Mathieu Yahiaoui (University of Melbourne, Australia)
William Mead (University of Melbourne, Australia)
Siyu Li (La Trobe University, Australia)
Yuyang Zhou (University of Melbourne, Australia)
Dr. Xiao Wang (Cornell University, US)
Owen Thompson (The University of Queensland, Australia)
Siris (Jingqi) Sun (University of Melbourne, Australia)
Jaco van Tonder (Tokyo University, Japan)

Program Structure:

For talks titles, abstracts, and recordings, please click on the below

Sponsors:
This symposium is supported by MATRIX and AMSI.