Week 17.11.2025 – 23.11.2025

The support propagation phenomenology of heat equations with multiplicative (white Gaussian) noise is well understood. If the noise coefficient is p-Hölder with p<1 at 0, the supports of non-negative solutions propagate with finite speed and hence are compact; if the noise coefficient is Lipschitz at 0, solutions are strictly positive, like those of the deterministic heat equation. After introducing this behaviour, I will first discuss its recent extension to stable, i.e. non-Gaussian, noises.

Next, we consider support propagation when the diffusion is replaced by a discontinuous motion. In this case, results from superprocess theory imply that at p = 1/2, solutions have unbounded supports. We prove that this is essentially sharp for a class of non-local stochastic evolution equations. In particular, if the noise coefficient is p-Hölder for p<1/2, the support of the solution is compact at almost all times. To prove this, we show that the process given by the solution integrated over certain half space spends most of its time at zero. This is done using an excursion decomposition of the local time at 0 of the (non-Markovian) spatially integrated process.

This talk includes joint ongoing work with Marcel Ortgiese.

Polyhedral manifolds are piecewise linear analogues of Riemannian manifolds. They are obtained by taking a collection of Euclidean simplices and identifying their hyperfaces by isometries. For example, the boundary of an n-dimensional Euclidean simplex is a polyhedral n-1-dimensional sphere. In this talk I'll speak about polyhedral Kahler manifolds, which are even dimensional polyhedral manifolds with unitary holonomy. While any Riemann surface has plenty of polyhedral Kahler metrics, the situation in complex dimension 2 and higher is very different. Such metrics seem to be very rare, and the known ones are related to the most rigid objects, such as complex reflection groups. The talk will be partially based on the recent work with Martin de Borbon, arXiv:2106.13224, arXiv:2411.09573, arXiv:2510.17447.

I will review some results on semi-classical quantization of M2 branes in AdS4 x  S7/Zk in their relation to dual   ABJM theory  and then  discuss  recent work on computing 2-loop corrections to world-volume S-matrix in superstring  and supermembrane theory.

Physical or biological processes can have input factors (such as temperature, pressure, etc.) that vary over time, i.e. they have a functional nature. If the output is also functional (such as activity or growth curves in biology or shape profiles in manufacturing), the relationship between the functional output and the dynamic factors can be modelled using function-on-function linear models.

In experimental settings, the functional form of the dynamic factors can be chosen by the experimenter, albeit with some constraints in terms of the complexity. In this talk, we will discuss how dynamic factors can be set in an optimal way to improve the accuracy of the estimators in function-on-function linear models. We will see how A-optimality and D-optimality (and their Bayesian versions) can be extended to this setting and what kinds of designs are optimal depending on the modelling choices on the functional objects.

This is joint work with Caterina May and Theodoros Ladas

Abstract: In this talk, we report on joint work in progress with Netan Dogra on the Zilber–Pink conjecture for curves inside abelian varieties, using a p-adic method. The Zilber–Pink conjecture can be viewed as a vast generalisation of well-known conjectures in Diophantine geometry, including the Mordell, Mordell–Lang, and André–Oort conjectures. We will begin with an overview of our approach in the context of Mordell–Lang for curves and discuss how it compares with that of Zilber–Pink.