Mon, 27 Apr 2026
16:30 -
17:30
L4
TBA
Dr. Andre Guerra
(Department of Applied Mathematics and Theoretical Physics University of Cambridge)
Abstract
TBA
Mon, 16 Feb 2026
16:30 -
17:30
L4
A finite-volume scheme for aggregation-diffusion equations with non-linear mobility
David Gomez-Castro
(UAM)
Abstract
The aim of this talk is to discuss a finite-volume scheme for the aggregation-diffusion family of equations with non-linear mobility
∂tρ = ∇ · (m(ρ)∇(U′(ρ) + V + W ∗ ρ)) in bounded domains with no-flux conditions. We will present basic properties of the scheme: existence, decay of a free, and comparison principle (where applicable); and a convergence-by-compactness result for the saturation case where m(0) = m(1) = 0, under general assumptions on m,U, V , and W. The results are joint works published in [1, 2]. At the end of the talk, we will discuss an extension to the Porous-Medium Equation with non-local pressure that corresponds to m(ρ) = ρm, U, V = 0 and W(x) = c|x|^−d−2s.
This project is joint work with Jose Carrillo (University of Oxford).
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Mon, 09 Feb 2026
16:30 -
17:30
L4
Scattering and Asymptotics for Critically Weakly Hyperbolic and Singular Systems
Dr. Arick Shao
(Queen Mary University of London)
Abstract
We study a very general class of first-order linear hyperbolic
systems that both become weakly hyperbolic and contain singular
lower-order coefficients at a single time t = 0. In "critical" weakly
hyperbolic settings, it is well-known that solutions lose a finite
amount of regularity at t = 0. Here, we both improve upon the analysis
in the weakly hyperbolic setting, and we extend this analysis to systems
containing critically singular coefficients, which may also exhibit
modified asymptotics and regularity loss at t = 0.
In particular, we give precise quantifications for (1) the asymptotics
of solutions as t approaches 0, (2) the scattering problem of solving
the system with asymptotic data at t = 0, and (3) the loss of regularity
due to the degeneracies at t = 0. Finally, we discuss a wide range of
applications for these results, including weakly hyperbolic wave
equations (and equations of higher order), as well as equations arising
from relativity and cosmology (e.g. at big bang singularities).
This is joint work with Bolys Sabitbek (Ghent).
Mon, 08 Dec 2025
16:30 -
17:30
L5
Improved regularity for nodal sets of Abelian Yang-Mills-Higgs equations.
Dr. Shengwen Wang
(Queen Mary University of London)
Abstract
We consider Yang-Mills-Higgs equations with U(1) gauge group. There is a deep relation between the adiabatic limit of a sequence of this physical PDEs and geometric PDE of minimal submanifolds. It is known that the energy measures are converging to a codimension 2 stationary varifold and the energy functional is converging to the codimension 2 mass. When the ambient dimension is \leq 4 or the sequence is minimizing, we can improve the weak convergence above and obtain strong regularity for the nodal sets that they are converging to the limit minimal submanifold with uniform $C^{2,\alpha}$ bounds. This is joint work with Huy Nguyen.
Thu, 20 Nov 2025
12:00 -
13:00
C5
Existence and weak-strong uniqueness of measure solutions to Euler-alignment/Aw-Rascle-Zhang model of collective behaviour
Ewelina Zatorska
(University of Warwick)
Abstract
I will discuss the multi-dimensional Euler–alignment system with a matrix-valued communication kernel, which is motivated by models of anticipation dynamics in collective behaviour. A key feature of this system is its formal equivalence to a nonlocal variant of the Aw–Rascle–Zhang (ARZ) traffic model, in which the desired velocity is modified by a nonlocal gradient interaction. The global-in-time existence of measure solutions to both formulations, can be obtained via a single degenerate pressureless Navier–Stokes approximation. I will also discuss a weak–strong uniqueness principle adapted to the pressureless setting and to nonlocal alignment forces. As a consequence of these results we can rigorously justify the formal correspondence between the nonlocal ARZ and Euler–alignment models: they arise from the same inviscid limit, and the weak–strong uniqueness property ensures that, whenever a classical solution exists, both formulations coincide with it.
Computing multiple solutions of systems of nonlinear equations with deflation
Farrell, P
Tue, 27 Jan 2026
12:30
12:30
C3
Electrostatic regulation of biomolecular condensates.
Jasper Knox
(Dept of Engineering Maths University of Bristol)
Abstract
Biomolecular condensates are membraneless assemblies of biomolecules (such as proteins or nucleic acids) formed through liquid-liquid phase separation. Many biomolecules are electrically charged, making condensates highly sensitive to the local electrochemical environment. In this talk, I will discuss our recent theoretical work on the dynamics of charged condensates and the role of salt concentration in their evolution toward equilibrium. Two-dimensional simulations of a thermodynamically consistent phase-field model reveal that salt can arrest coarsening by affecting the relative strength of interfacial energy, associated with the condensate surface, and electrostatic energy, arising from the formation of an electric double layer across liquid interfaces. At low salt concentrations, the electrostatic energy of the double layer becomes comparable to the interfacial energy, resulting in the emergence of multiple condensates with a fixed size. These results show that salt can act as a dynamic regulator of condensate size, with implications for both understanding biological organisation and modulating the behaviour of synthetic condensates.