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| Name |
Title |
Date |
Time |
Room |
| 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 |
| Fraser Sanders (The University of Manchester) | Infinite-dimensional contact geometry and conservative contact systemsAbstract: In finite dimensions, contact geometry is well-studied as an odd-dimensional counterpart to symplectic geometry. It is also a natural setting in which to generalise Hamiltonian mechanics of systems, taking into account a notion of dissipation or diffusion. For example, the simplest example of a contact-Hamiltonian system is the damped harmonic oscillator (the dissipative counterpart to the simple harmonic oscillator). Due to the diffusive properties of the contact-Hamilton equations, it is also a natural setting in which to study thermodynamics (cf. Grmela, Bravetti, and many others). In fact, the 1st law of thermodynamics, $dU = T dS$ can be considered as defining a contact form on $\mathbb{R}^3$.
The goal during the seminar is to show that contact geometry can be meaningfully defined in infinite-dimensional manifolds, and to give some elementary examples of infinite-dimensional contact Hamiltonian systems.
Time permitting, I will also discuss some subset of
- Interesting differences between finite- and infinite-dimensional contact geometry,
- Infinite-dimensional counterparts of Hopf fibrations,
- And how to define a large class of conservative contact systems, and some examples of this concept. |
Tuesday, 17 November 2026 |
13:00 - 14:00 |
HXLY 145 |
| David Parmenter (University of Bristol) | TBDAbstract: TBD |
Tuesday, 24 November 2026 |
13:00 - 14:00 |
HXLY 145 |
| Tresnia Berah (Imperial College London) | Selection principles for quasi-stationary distributions and reinforcement processesAbstract: Let $P$ be a sub-Markov matrix on a finite set $S$.
We study a reinforced process that evolves according to $P$ until
absorption and is then resurrected at a point sampled from its weighted
past occupation measure $\mu_n$, with positive weights $w_k$ and
cumulative weights $W_n = w_0 + \cdots + w_n$.
Whereas the irreducible case leads to almost sure convergence towards
the unique quasi-stationary distribution (QSD), we consider reducible
kernels, for which several QSDs may coexist.
Under generic assumptions on $P$ and suitable assumptions on the
weights and initial condition, there are finitely many QSDs and the
asymptotic selection is governed by the summability of $1/W_n$.
If the series $\sum_{n=0}^{\infty} 1/W_n$ diverges, then $\mu_n$
converges almost surely towards the QSD associated with the largest
Perron value.
If the series converges, then $\mu_n$ converges almost surely towards
a QSD, and each QSD is selected with positive probability.
For polynomial weights $w_0 = 1$ and $w_k = k^q$ for $k \geq 1$,
the first regime corresponds to $-1 \leq q \leq 0$ and the second
to $q > 0$. |
Tuesday, 1 December 2026 |
13:00 - 14:00 |
HXLY 145 |
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