MATRIX Research Program: Log-gases in Caeli Australi: Recent Developments in and Around Random Matrix Theory

Organisers:

• Anas Rahman (The University of Hong Kong)
• Jiyuan Zhang (South China University of Technology)
• Sylvia Serfaty (New York University, Courant Institute / Sorbonne Université)
• Alice Guionnet (Ecole Normale Superieure de Lyon)
• Mario Kieburg (The University of Melbourne)
• Lucas Hackl (The University of Melbourne)

Description:

With sufficiently poetic allowances, the milky way — a treasure of the southern heavens sought by many a gaze worldwide — can be seen as a log-gas in caeli australi. Here, a log-gas refers to a system of particles, oftentimes arising as eigenvalues of random matrices, that interact pairwise with logarithmic strength. Being such fundamental topics, it is no surprise that the study of log-gases and random matrices is intertwined with numerous fields, many of which have risen to remarkable prominence in recent years.

The goal of this program is to bring together world-leading specialists on topics contiguous to random matrix theory for the purposes of sharing recent breakthroughs and initiating collaborations across multiple disciplines. Research activities will focus on relations between random matrix theory and the following five themes: statistical mechanics of log-gases; machine learning and statistical inference; (free) probability theory; orthogonal polynomials and asymptotic analysis; and integrable systems including Painleve equations.

This program will run for two weeks, with mornings reserved for talks and afternoons for collaborative discussion sessions led by distinguished leaders of their respective fields. The talks in the first week will focus on the dissemination of cutting edge research and the advertisement of open problems amenable to interdisciplinary research efforts, while the second week will give the remaining participants ample opportunity to share their recent achievements and otherwise network with a truly international community. Indeed, by providing an environment conducive to intensive research between Australian mathematicians (across all career stages) and their (long-standing and/or potential) international colleagues, this program will contribute greatly towards bridging the geographical gap between the relevant research communities in and outside Australia.

 

This MATRIX Research Program is partially supported by AMSI and AustMS through the AMSI-AustMS Workshop Funding program, and benefits from the SMRI International Visitor Program.

 

Registration:

• Registration is now closed
• Arrival date: 3 August 2025
• Departure date : 15 August 2025

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ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 5 August 2025
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.