PhD Student Symposium: Mathematical Structures in Statistical Mechanics

Over the last century, models of statistical mechanics have inspired a tapestry of rich mathematical structures. While mathematicians study the Ising model, percolation, and the six-vertex model for their inherent mathematical beauty, these models also serve to emulate real and universal physical phenomena. Our aim is to explore the mathematical frameworks that underpin select models of statistical mechanics, discussing recent advancements and their applications. We hope to encourage participation from Australian PhD students by exposing them to their international peers as well as renowned experts.

The focus topics of the symposium are:
1. Probability theory and its applications to the study of critical phenomena in models of statistical mechanics, including interacting particle systems and percolation.
2. The mathematics of integrable systems, including vertex models, dimer models, and quantum spin chains, as well as the applications of integrability to symmetric functions, representation theory, Temperley-Lieb algebras, and integrable probability.

We invite contributions that bridge the gap between probabilistic and algebraic perspectives, fostering collaboration and advancing our understanding of these complex systems.

Masterclass lectures:
Tim Garoni (Monash University)
“Statistical Mechanics in High Dimensions”
Michael Wheeler (University of Melbourne)
“The Schur Process and Limit Shapes”

Featured speakers:
Tim Banova (University of Melbourne)
Yucheng Liu (University of British Columbia, Canada)
Madeline Nurcombe (University of Sydney)
Sri Tata (Yale University, USA)
Dmitry Kolyaskin (Australian National University)

Organisers:
William Mead (University of Melbourne)
Aram Perez (Monash University)
Yuyang Zhou (University of Melbourne)

This symposium is supported by MATRIX and AMSI through the MATRIX-AMSI PhD Student Research Collaboration Scheme: matrix-inst.org.au/phd-student-research-collaboration-scheme-guidelines/