This seminar series gives visitors and staff members the opportunity to explain the context and aims of their work. These research talks cover any field in the mathematical sciences, and should be presented in a way that is understandable and interesting to a broad audience. Seminar information and recordings can be found below and in the SMRI Seminar YouTube playlist.
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SMRI Seminar ‘Singularities in fluid: Self-similar analysis, computer assisted proofs and neural networks’
Tristan Buckmaster, Courant Institute of Mathematical Sciences, New York University
Thursday 27 March 2025
Abstract: In this presentation, I will provide an overview of how techniques involving self-similar analysis, computer assisted proofs and neural networks can be employed to investigate singularity formation in the context of fluids.
SMRI Seminar ‘Hausdorff dimension of the Apollonian gasket’
Caroline Wormell, The University of Sydney
Thursday 27 February 2025
Abstract: The Apollonian gasket is a well-studied circle packing, created by iteratively filling a region with mutually tangent circles. Important properties of the packing, including the distribution of the circle radii, are universal and governed by its Hausdorff dimension. No closed form is currently known for the Hausdorff dimension, and its computation is a special case of a more general and hard problem: effective, rigorous estimates of dimension of a limit set generated by non-uniform contractions. In this talk, I will talk about an efficient method for solving this problem. With this method we can not only compute the dimension of the gasket to a lot of decimal places, but also rigorously validate this computation as a mathematical theorem. Our method is not particularly specialised to the Apollonian gasket, and could generalise easily to other “difficult” parabolic fractals. Based on joint work with Polina Vytnova.
SMRI Seminar ‘Coupled Chaotic Maps and Self-Consistent Transfer Operators’
Matteo Tanzi, King’s College London
Thursday 6th March 2025
Abstract: At the end of the 1980s, globally coupled maps (GCMs) emerged as high-dimensional models for complex systems. These models feature simple equations where several variables are coupled symmetrically all-to-all, and display a rich variety of behaviors, including synchronization, phase ordering, and turbulence. Rigorous mathematical studies of the dynamics of GCMs have primarily focused on their mean-field limit—that is, the behavior of the system’s average state as the number of maps approaches infinity. This limit is governed by a nonlinear operator known as the self-consistent transfer operator, which dictates the evolution of the mean field. In this talk, I will provide a brief overview of the origin of the study of self-consistent transfer operators and discuss some recent progress in the field focusing on coupled chaotic maps.