PostgraduateResearchDay

May 12, 2026
MCS 0001

The Durham Maths postgraduate research day is a celebration of the research being done by postgraduates in the department. It is an opportunity for students and postdocs to present their work to their peers via short accessible talks and to learn about the research being done by others.

Schedule (tentative)

Abstracts

Victoria Pelayo Avlaredo - Concentration and Median Leaves

We briefly recall the Lévy–Gromov concentration phenomenon under a positive lower Ricci curvature bound. We then discuss how, in the setting of codimension one singular Riemannian foliations, concentration can be localized near distinguished regular leaves.

Hei Jie Lam - Game Theory with a lot of players 

In this talk I will explain the basic concepts of Nash equilibria in games with finite number of players and the corresponding limiting problem when we would like to approximate a game with many players using a mean field approach. We will then discuss some real world applications of Nash equilibrium theory.

Yue Jiang - A sub-Riemannian flavored dynamic optimal transport problem

In this talk, I shall present a dynamic optimal transport problem arising from the linear control system (something more applicable to real life) which is endowed naturally a sub-Riemannian structure. I will also present its equivalence to a static optimal transport problem. Moreover, it turns out that the equivalence extends to the uniqueness of minimiser of the two variational problems. Basics on optimal transport theory and sub-Riemannian geometry will be briefly revisited.

Shrog Albalawi - Assessing variable influence on change points in sparse high-dimensional data

Detection of change points in sequences of high-dimensional observations remains a challenging problem, especially in sparse settings where only a small subset of variables may be affected. Beyond detecting whether a significant change point is present and estimating its location, the main objective is to identify which variable, or group of variables, drives the detected change point. This work studies the problem in a post-detection setting, where variables are grouped according to a chosen criterion and their relation to the detected change point is then examined. Such grouping provides a natural way to reduce dimensionality from p variables to K groups, with K < n ≪ p, while improving the interpretability of sparse high-dimensional data. Numerical simulations illustrate the performance of this framework and indicate improved results as the sample size and signal strength increase.

Samuel Shepherd - Green Currents of Cycles on Unitary Shimura Varieties

We discuss the problem of constructing Green forms for special cycles on locally symmetric spaces associated to unitary groups. In the latter part of the talk, we discuss recent work on the integrals of these forms over the full space, and over smaller cycles within it.

Tianlin Yang - A Distribution-to-Distribution Neural Framework for Probabilistic Forecasting of Dynamical Systems

This talk presents a distribution-to-distribution neural framework for probabilistic forecasting in dynamical systems. Instead of predicting individual trajectories, the method models the evolution of predictive distributions directly, allowing uncertainty to be represented and propagated in a unified way. I will also briefly show results from the Lorenz63 system to illustrate its ability to capture nonlinear distributional dynamics.

Zhaocheng Li - Bayes Linear Analysis to Models with Multi-partial Discontinuities with UQ

The simulation for real-world systems can be computationally intensive or even infeasible to compute the acceptable parameters. We analytically build an emulator using the Bayes Linear Analysis to adjust the expectation of our output, provide the uncertainty quantification, and achieve the feasibility to surrogate the simulator. This methodology hardly works with the scenario of models that are partially discontinuous, as its exponentialized kernel functions are at least continuous and more-or-less differentiable. We will provide some possible extensions with statistical estimates to adjust our running input design to solve some typical cases.

Joseph Marshall - A Flat Pack Universe

In particle physics we have a problem: our theories are too good. For around 100 years now, quantum mechanics (and later, quantum field theory (QFT)) have provided us with the framework to make predictions for phenomena to very high energies with very high precision, and, barring a few notable exceptions, the experiments keep agreeing with theory as well as could be hoped. This sounds like a nice problem to have, but of course we also know that QFT can’t be the whole story, as it doesn’t provide a consistent quantum description of gravity. One place to look that may give us some insight into how the two interact is the very early universe, when gravity was incredibly important and small quantum fluctuations were blown up to large scales, seeding perturbations that can be observed today. In this talk, I aim to give a (very) brief and introductory look at quantum mechanics and cosmology, followed by a surface overview of the framework developed in my research in which quantum objects in the early universe can be directly related to those in “flat space” (in the absence of gravity). I aim to review these topics at a very basic and pedagogical level, assuming only a familiarity with linear algebra.

Yanpeng Zhi - Elliptic Phi_4^4 Model with Boundary Blow-up: Triviality and Renormalization

Phi^4 model refers to a class of stochastic PDEs related to construction of Phi^4 Euclidean quantum field theory. They involve cubic non-linearity, driven by white noise and usually called stochastic quantization equations. There has been extensive research on parabolic and hyperbolic Phi_2^4 models, where the subscript "2" means 2-dimensional domains. In this talk, I will present my recent work for elliptic models on the 4-dimensional hypercube, imposed with an infinity boundary condition. Without renormalization, the regularised equations will converge to something deterministic as white noise recovers, which is the triviality property shared with parabolic and hyperbolic settings. The limit is a PDE if noise intensity is weak, and is zero if noise strength is strong. To find a meaningful stochastic object solving elliptic models, we will prove existence of renormalized solutions. This requires renormalizing suitably the non-linear term in equations, and yields non-trivial limits as noise regularisation is removed.

Jeremy Cai - Mathematics of SAXS with an application to Protein RNA docking

Proteins and their complexes participate in almost all biological processes required for life, such as, molecular binding, transport and chemical catalysis. Recently deep learning methods, mainly trained on known, X-ray crystallographic structures, such as AlphaFold 3 have predicted static protein and protein complex structures when given amino and nucleic acid sequences as input. However, these methods perform poorly with protein RNA complexes since there is a lack of experimentally resolved structures at atomic resolution and molecular flexibility. Small Angle X-ray Scattering (SAXS) is a low resolution experimental technique which observes biomolecules under near native solution conditions. This gives an underdetermined scattering curve which encodes information on the size and shape of the biomolecule as well as a pairwise distance distribution of electron density. In this talk we present some work on Protein RNA docking using SAXS data. Firstly, we introduce the mathematics behind SAXS scattering calculations and curve fitting. Then, given initial structures of high atomic resolution, we propose a method for the protein RNA docking search. Finally, we test our method on a known complex: NS1 protein of influenza B virus bound to 5’ triphosphorylated dsRNA.

Organizers

Feel free to direct any questions or comments to:

• Tahani Coolen-Maturi
• Jack Shotton
• Peter Wyper
• Sam Jackson