This term, all seminars take place Thursdays at 2pm, room MS.04 (Zeeman Building), unless indicated otherwise.

Schedule for

Sasha Sodin, 08.06.2017


25.04.2019 Olga Izyumtseva (QMUL)
Self-intersection local time for compactly perturbed Wiener processes
We consider Gaussian processes obtained as the compact perturbations of Wiener process. Increments of compactly perturbed Wiener process on small time intervals have similar behaviour to the behaviour of increments of Wiener process. The law of iterated logarithm and asymptotics of small ball probabilities can be established for it. The main advantage of introduced class of Gaussian processes is the possibility to construct Rosen renormalization for the self-intersection local times in the planar case. We present the corresponding statement in terms of Fourier-Wiener transform.
The talk is based on the joint works with Andrey Dorogovtsev.

Contact: Daniel/Stefan G
02.05.2019 Nicolas Dirr (Cardiff)
A Stochastic porous medium equation with divergence form noise
We construct nonnegative martingale solutions to the stochastic porous medium equation in one space dimension by introducing a (spatial) semi-discretization and establishing convergence, based on energy estimates.
Contact: Stefan A
09.05.2019 Erik Slivken (Paris)
Neighborhood Growth on the Hamming plane
We introduce a generalized growth model on two-dimensional Hamming graphs that accounts for long-range interactions. We start with a collection of occupied sites on Z_+^2. The decision to add a point at a site is made by counting the number of currently occupied points on the horizontal and the vertical line through it, and checking whether the pair of counts lies outside a fixed Young diagram. This process can be viewed as a generalization of bootstrap percolation. We study a of number of extremal quantities. Some natural, like the smallest spanning set or the slowest spanning set; others related to the probability that a rectangle will be spanned by a given density of initially occupied sites. This is joint work with Janko Gravner, J.E. Paguyo, and David Sivakoff.
Contact: Oleg

No seminars (Warwick-Cergy meeting)

30.05.2019 Matthew Dickson (Warwick)

Contact: Stefan A
06.06.2019 Sabine Boegli (Imperial College)
Schroedinger operator with non-zero accumulation points of complex eigenvalues
We consider Schroedinger operators on the whole Euclidean space or on the half-space, subject to real Robin boundary conditions. I will present the construction of a non-real potential that decays at infinity so that the corresponding Schroedinger operator has infinitely many non-real eigenvalues accumulating at every point of the essential spectrum. This proves that the Lieb-Thirring inequalities, crucial in quantum mechanics for the proof of stability of matter, do no longer hold in the non-selfadjoint case.
Contact: Daniel
13.06.2019 Eleanor Archer (University of Warwick)
Brownian motion on looptree-type structures
The study of percolation models on random planar maps gives important insights into the behaviour of random surfaces. In this talk, we will start by reviewing some background on random maps, with particular emphasis on the Brownian universality class and associated percolation models. It turns out that in this regime, critical percolation clusters are closely related to a class of random objects called looptrees, which will be the central objects of this talk. In particular, we will outline some of their key volume growth properties, and discuss a scaling limit result for random walks on looptrees, including giving a construction of the limiting diffusion. We will conclude by exploring applications of these looptree results, for example to outerplanar maps, and to the study of random walks on critical percolation clusters.
Contact: Daniel