PostgraduateResearchDay 2024

May 22, 2024
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)

Registration

To register, please fill out the following form: link.

Abstracts

Abdulmajeed Alharbi - Optimal Threshold Selection Using Nonparametric Predictive Inference

Medical applications require the selection of an appropriate threshold to diagnose patients as either diseased or healthy, depending on their test results. A nonparametric predictive approach, called NPI, has been introduced. The NPI method differs from classical methods in the literature in that the inferences are explicitly based on a given number of future individuals. NPI-based methods are introduced for selecting the optimal diagnostic test threshold for two-group classification and have shown some promising results that overcome some limitations in classical methods.

Arron Bale - Simple topological tools for complex protein folding problems

I will introduce the protein folding problem and the small angle X-ray scattering (SAXs) approach we take. I will then describe some of the topological tools I've used to constrain this problem. I will finish by highlighting some of the remaining challenges in this area, hopefully encouraging others to bring their expertise to get involved with this project.

Thomas Bartsch - Generalised symmetries in quantum field theory

Symmetries provide a powerful tool for our understanding of quantum systems in nature. While traditionally described by the theory of groups and their representations, a generalised notion of symmetry discovered over the course of the past decade can be captured using higher category theory. In this talk, I will introduce this notion of generalised symmetries and discuss their action on the (extended) operator content of generic quantum systems.

Alexander Jackson - Affine group schemes and polynomial problems

Given a ring R, there are many ways we can define a corresponding group, for example GL_n(R) or SL_n(R). We can think of GL_n, SL_n, etc. as objects in their own right, which take in a ring and output a group. For such an affine group scheme G and finite field F_q such that G(F_q) is defined, we can consider the infinite sequence of groups G(F_{q^d}) for d=1,2,3... . We ask whether one can describe the dimensions of the irreducible representations of all these groups at once using finitely many polynomials, and give a partial answer. In the case of GL_n, this relates to a conjecture of Onn (2008).

Iolo Jones - Diffusion Geometry for Data Analysis

In this talk, I will introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry defines a theory of Riemannian geometry on a wide range of probability spaces and allows us to estimate that geometry from data, so can be used as a general tool for geometric machine learning and statistics. We find that diffusion geometry outperforms existing methods as a biomarker for real and simulated tumour histology data and can robustly detect singularities in manifold-like data.

Navonil Neogi - Wilson lines and extended operators in CFT

Conformal field theories (CFTs) are a class of quantum field theory with particular interest in theoretical physics, as well as condensed matter physics, and are crucial in statistical physics generally. In this talk, I will sketch how quantum electrodynamics in 3 dimensions can be considered in a limit where it describes a CFT, the physical relevance of this, and what operators mean in this theory - including a sketch of nonlocal ones, which I am especially concerned with in my research.

Guy Parker - Convexity on the space of probability measures

When we study a system of interacting agents, particles often evolve according to some energy minimisation principle. To understand the evolution of the system, we would like to quantify certain properties of this energy. For example, does the energy have a minimum and, if so, is this minimum unique? In this talk, I discuss how such energies may often be realised as functions on the space of probability measures and, subsequently, compare notions of convexity on this space, relating these properties to the behaviour of the physical system.

Jost Pieper - Rough paths, sewing and rough stochastic calculus

The theory of rough paths developed by Terry Lyons in the 90’s established a framework for differential equations and the corresponding integration for low regularity driving noises which admits desirable continuity properties of the solution maps with strong ties to the theory of stochastic analysis. In this talk I will introduce the basic notions of rough paths including different versions of the sewing lemma as the main tool for the construction of integrals. Additionally, I will provide a brief overview of the diverse applications in stochastic analysis and explore recent advancements in the jointly stochastic and rough theory of rough stochastic differential equations.

Giorgio Pizzolo - Double Copy and L_infinity algebras

In this talk, I will give a very brief introduction to the field I am working in, Double Copy theory. I will describe how the idea behind this theory emerged and why it has captured the imagination of physicists around the globe. Then, I will discuss one of the projects my supervisor and I are working on, which involves using an algebraic formulation of gauge theories to write a double copy prescription.

Rafail Psyroukis - Modular Forms and applications

In this talk, we will discuss basic facts about classical modular forms. We will give the main definitions and then proceed to discuss how they can be used in order to answer some classical problems of mathematics such as the number of representations of a number as a sum of squares and Fermat's Last Theorem.

Tianlin Yang - Correcting of predictive Machine Learning and Imperfect Physical models

In the fast-paced world of today, artificial intelligence technology has made leaps and bounds in recent years. In the present day, scientists are attempting to apply machine learning methods to solve a number of practical challenges. Although machine learning method have good performance, we believe that the outcomes of classical physical model simulations coupling machine learning prediction result would be better. This presentation focuses on investigate the feasibility of coupling physical models and machine learning methods, that is, the extent to which machine learning models can correct for errors in imperfect and perfect physical models.

Yingjuan Zhang - A nonlinear latent variable model with applications to principal curve fitting

I will present a non-linear model that approximates non-linear multivariate data structures through the use of a smooth curve. Both simulated and real data will be used for comparison with principal curves, illustrating how a random effect model can be employed to estimate principal curves.

Organizers

Feel free to direct any questions or comments to:

• Shrog Albalawi
• Mathew Bullimore
• Tahani Coolen-Maturi
• Yue Ren