This term, all seminars take place Thursdays at 2pm, room MS.03 (Zeeman Building), unless indicated otherwise.

Schedule for

Matthew Dickson, 30.05.2019


11.01.2024 (Talk cancelled, because of abrupt change of flight schedule)

18.01.2024 Josephine Evans (University of Warwick)
Non-Equilibrium steady states in BGK models for gas dynamics
This talk is based on a joint work with Angeliki Menegaki from Imperial. We consider the BGK kinetic model for a dilute gas coupled to a thermostat modelling gain and loss of kinetic energy for the particles. I will discuss how to show existence and linear stability for a model of this type and also why stability results are difficult in this area and how such results are related to one way of deriving the Fourier law from microscopic processes.
Contact: Vedran
25.01.2024 Tomohiro Sasamoto (Tokyo Institute of Technology)
Macroscopic fluctuation theory for the symmetric simple exclusion process and a classical integrable system
The large deviation principle for symmetric simple exclusion process(SEP) had been established by Kipnis, Olla, Varadhan in 1989 [1]. A somewhat different formulation, known as the macroscopic fluctuation theory (MFT), was initiated and developed by Jona-Lasinio et al in 2000’s [2]. The basic equations of the theory, MFT equations, are coupled nonlinear partial differential equations and have resisted exact analysis except for stationary situation. In this talk we introduce a generalization of the Cole-Hopf transformation and show that it maps the MFT equations for a few symmetric diffusive systems including SEP to the classically integrable Ablowitz-Kaup-Newell-Segur(AKNS) system. This allows us to solve the equations exactly in time dependent regime by adapting standard ideas of inverse scattering method. The talk is based on a joint work with Kirone Mallick and Hiroki Moriya [3]. References [1] C. Kipnis, S. Olla, S. R. S. Varadhan, Hydrodynamics and large deviations for simple exclusion processes, Comm. Pure Appl. Math., 42:115–137, 1989. [2] L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Macroscopic fluctuation theory, Rev. Mod. Phys., 87:593–636, 2015. [3] Kirone Mallick, Hiroki Moriya, Tomohiro Sasamoto, Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process. Phys. Rev. Lett. 129 (2022)
Contact: Matteo
01.02.2024 Markus Tempelmayr (University of Münster)
Malliavin calculus and regularity structures
We give an overview of some probabilistic aspects of the solution theory for singular SPDEs, following the recent approach of Otto, Sauer, Smith and Weber. The basic idea is to parameterize the model, which captures the local solution behaviour, by partial derivatives w.r.t. the nonlinearity. Malliavin calculus plays a prominent role, on the one hand to obtain convergence of renormalized models based on a spectral gap assumption of the driving noise, on the other hand to obtain a characterization of models establishing a universality-type result. Based on joint work with Lucas Broux, Pablo Linares, Felix Otto and Pavlos Tsatsoulis.
Contact: Nikos

15.02.2024 Andreas Koller (University of Warwick)
Scaling limit of gradient models on $Z^d$ with non-convex energy
Random fields of gradients are a class of model systems arising in the study of random interfaces, random geometry, field theory and elasticity theory. The models we consider are characterised by an imposed boundary tilt and the free energy (called surface tension in the context of random interface models) as a function of tilt. Of interest are, in particular, whether the surface tension is strictly convex and whether the large-scale behaviour of the model remains that of the massless free field (Gaussian universality class). Where the Hamiltonian (energy) of the system is determined by a strictly convex potential, good progress has been made on these questions over the last two decades. For models with non-convex energy fewer results are known. Open problems include the conjecture that, in any regime of the parameters such that the scaling limit is Gaussian, its covariance (diffusion) matrix should be given by the Hessian of surface tension as a function of tilt. I will survey some recent advances in this direction using renormalisation group arguments and describe our result confirming the conjectured behaviour of the scaling limit for a class of non-convex potentials in the regime of low temperatures and small tilt. This is based on joint work with Stefan Adams.
Contact: Stefan
22.02.2024 Olga Iziumtseva (University of Nottingham)
Asymptotic and geometric properties of Volterra Gaussian processes
In this talk we discuss properties of Gaussian processes with the representation int_0^t c(t,s) dG(s), where G is a continuous Gaussian martingale, and c is a square-integrable Volterra kernel. Volterra Gaussian processes described in terms of a stochastic integral with respect to a Wiener process were first introduced by P. Lévy in 1956 as the canonical Volterra representation for a given Gaussian process, and continue to be an active area of research. In this talk we establish the law of iterated logarithm for a one-dimensional Volterra Gaussian process, we discuss the existence of local time in dimensions d > 1, and construct the Rosen renormalized self-intersection local time for a planar Volterra Gaussian process.
Joint work with Wasiur Khudabukhsh.

Contact: Daniel
29.02.2024 Pierre Germain (Imperial College London)
Kinetic wave equations
Kinetic wave equations are to waves what Boltzmann is to particles: they describe the out of equilibrium statistical mechanics of nonlinear wave (or dispersive) equations. As such, they provide an entry point to the analysis of turbulent regimes in such systems. I will try and give an overview of the field, which has seen rapid progress in the last few years.
Contact: Vedran
07.03.2024 Stefan Grosskinsky (University of Augsburg)
Size-biased diffusion limits and the inclusion process
We study the Inclusion Process with vanishing diffusion coefficient, which is a stochastic particle system known to exhibit condensation and metastable dynamics for cluster locations. We focus on the dynamics of the empirical mass distribution and consider the process on the complete graph in the thermodynamic limit with fixed particle density. Describing a given configuration by a measure on a suitably scaled mass space, we establish convergence to a limiting measure-valued process. When the diffusion coefficient scales like the inverse of the system size, the scaling limit is equivalent to the well known Poisson-Dirichlet diffusion. Our approach can be generalized to other scaling regimes, providing a natural extension of the Poisson-Dirichlet diffusion to infinite mutation rate. Considering size-biased mass distributions, our approach yields an interesting characterization of the limiting dynamics via duality.
This is joint work with Simon Gabriel (Münster) and Paul Chleboun (Warwick).

Contact: Daniel
14.03.2024 Tyler Helmuth (University of Durham)

Contact: Vedran