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About the School

Abstracts

Serena Dipierro
Professor and Head of the Department of Mathematics and Statistics @ the University of Western Australia.
Serena Dipierro took her PhD in Mathematical Analysis @ the International School for Advanced Studies (SISSA, Trieste) in 2012. After PostDoc positions @ the Universidad de Chile and University of Edinburgh, and a Humboldt Fellowship, she held permanent positions @ the University of Melbourne and the Università di Milano. In August 2018 she moved @ the University of Western Australia, where she is now Professor and Head of the Department of Mathematics and Statistics.
Boundary behaviour of nonlocal minimal surfaces

In this talk we present a peculiar behaviour of nonlocal minimal surfaces (i.e. local minimisers of a nonlocal perimeter functional), namely the capacity, and the strong tendency, of adhering to the boundary of the reference domain. This characteristic is in contrast not only with the boundary behaviour of classical minimal surfaces but also with the pattern produced by solutions of linear equations. We will discuss this phenomenon and present some recent results.

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Professor @ the Beijing Institute of Technology.
Rongchan Zhu got her Phd in 2021 @ Chinese Academy of Science and Bielefeld University. Now, she is professor @ the Beijing Institute of Technology.
Large \(N\) Limit of the \(O(N)\) Linear Sigma Model via Stochastic Quantization

In this talk, I will discuss large \(N\) limits of a coupled system of \(N\) interacting \(\Phi^4\) equations posed over \(\mathbb{T}^{d}\) for \(d=1,2,3\), known as the \(O(N)\) linear sigma model. Uniform in \(N\) bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well-posed. Moreover, I show tightness of the invariant measures in the large \(N\) limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order \(1/\sqrt{N}\) with respect to the Wasserstein distance.

I will also consider fluctuations and obtain tightness results for certain \(O(N)\) invariant observables, along with an exact description of the limiting correlations in \(d=1,2\).

This talk is based on joint work with Hao Shen, Scott Smith and Xiangchan Zhu.

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