STAFF
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| Name |
Title |
Date |
Time |
Room |
| Arthur Limoge (Surrey Space Centre, University of Surrey) | The twist condition in the three-body problemAbstract: A famous method for finding periodic orbits of dynamical systems, which we owe to Poincaré, is through fixed point theorems, most of which rely on some form of "twist condition". In the case of the spatial (circular restricted) three-body problem, this twist condition is a geometric assumption on some 4-dimensional (symplectic) manifold. In this talk, I will describe a conjecture regarding this twist condition whose veracity would yield existence of infinitely many periodic orbits — an open problem to this day. This will be done with a minimum amount of technical details, so that the conjecture can be made accessible to people with little to no background in differential geometry or physics. |
Tuesday, 20 October 2026 |
13:00 - 14:00 |
HXLY 145 |
| George Stepaniants (University of Cambridge) | Volterra Integral Equations and Memory Dependent Constitutive LawsAbstract: We will discuss how Volterra integral equations arise naturally in partially observed dynamical systems with specific applications to multiscale materials. This will motivate the construction of surrogate machine learning operators for the time-dependent simulation of multiscale materials. Finally, we will explore new developments in the theory of Volterra integral equations and the insights they gives us into the nonlinear operators that these surrogates approximate.
Bio:
George Stepaniants is an Assistant Professor in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Previously, he was an NSF Mathematical Sciences Postdoctoral Research Fellow in Computing and Mathematical Sciences at Caltech and received his PhD in Mathematics from MIT in 2024. His research spans applied analysis, inverse problems, optimal transport, and scientific machine learning. |
Tuesday, 27 October 2026 |
13:00 - 14:00 |
HXLY 145 |
| Nicolas Boulle (Imperial College London) | A zero-one law for one-shot system identificationAbstract: Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differential operators and dynamical systems. For a single input-response pair, recovery is possible exactly when the evaluated dictionary terms are linearly independent. We prove a sharp zero-one law: either no input uniquely determines the coefficients, or almost every random input sampled from a nondegenerate Gaussian measure does. This dichotomy reduces one-shot system identification to a question about degenerate inputs and provides an a posteriori certificate for any recovered model. Numerical examples recover dynamical systems, nonlinear partial differential equations, and structured matrix families from single trajectory data, while also detecting when an extra probe is necessary. |
Tuesday, 10 November 2026 |
13:00 - 14:00 |
HXLY 145 |
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