Federico Cornalba

Dr Federico Cornalba

Federico’s research sits at the intersection between stochastic analysis, numerical analysis, and PDE theory. Primarily, he is interested in describing large-scale interacting particle systems (these are ubiquitous in a whole range of applications in physics, social/opinion dynamics, and more) by using equivalent continuous models (often in the form of stochastic equations). These continuous models are, in general, more tractable than the particle models they stem from, especially when it comes to computational costs and specific interpretability features. He deploys methods from stochastic analysis, numerical analysis, and PDE theory to study relevant aspects of these continuous models. He is also interested in Machine Learning tools: so far, he has researched Deep Reinforcement Learning methods for asset-trading applications.

Research interests:

  • Modelling of large-scale interacting particle systems
  • Analysis and numerics of stochastic PDEs of Fluctuating Hydrodynamics
  • Reinforcement Learning methods

 

LINKS:

Federico Cornalba on the University of Bath Research Portal

Dr Avi Mayorcas

Broadly my research tends to lie at the intersection of stochastic analysis and partial differential equations (PDE). This might mean studying certain stochastic PDE with connections to deterministic phenomena or studying properties of deterministic PDE via associated finite dimensional stochastic dynamics; think of the Feynman-Kac relationship between Brownian motion and the heat equation. Currently, I am concretely interested in three main areas: regularisation by noise phenomena – whether stochastic dynamics enjoy improved properties over their deterministic counterparts; stochastic quantisation of physical field theories and applications of stochastic analysis to game theory and macroeconomics. In addition, I have interests that are adjacent to the above, or at times combine some of them. If any of this sounds appealing, please do get in touch and I’d be happy to discuss further.

Research interests:
  • Regularisation by noise in stochastic partial and ordinary differential equations
  • Stochastic quantisation of physical field theories
  • Game theory and mean field dynamics in macroeconomics and finance

LINKS:

Avi Mayorcas on the University of Bath Research Portal

Dr Christoforos Panagiotis

I am interested in mathematical models arising from statistical physics both in the classical setting of the hypercubic lattice and more generally on groups. This specifically includes percolation, the Ising model, the Potts model, the Blume-Capel model, self-avoiding walk, and Abelian sandpile percolation.

 

Research interests: 

  • Percolation and lattice spin models
  • Probability on groups
  • Self-avoiding walk

 

LINKS:

Dr Matthew Schrecker

Much of my research to date has focused on the compressible Euler equations. The Euler equations have a rich mathematical structure underpinning one of the most basic physical processes in the universe: the flow of gases. Over the past 250 years, the equations have inspired developments in mathematical analysis, functional and harmonic analysis, dynamical systems and geometric analysis. The Euler equations are also relevant in understanding phenomena in the physical world ranging from the flow out of an exhaust pipe to the motion of galaxies and collapse of stars. In all of these physical processes, the formation of shock waves is a ubiquitous phenomenon (as seen physically, for example, in a sonic boom coming from a Concorde aircraft) that causes a drastic loss of regularity in solutions of the system. The presence of shocks has led to the need to study weak solutions of the Euler equations, as classical (differentiable) solutions will generically blow up in finite time, and so my research has focused on both of these aspects: the existence of weak solutions and the properties and behaviour of smooth solutions on approach to singularity formation. More recently, I have also been working on the problem of the gravitational collapse of stars, a different type of singularity formation in which the physical variables of the system (particularly the density of a star) blow up in finite time as matter falls in towards the centre of the star. Such a phenomenon is also modelled with the Euler equations, but now with a gravitational field as well.

 

Research Interests:

  • Analysis of Partial Differential Equations
  • Fluid dynamics (especially free boundary problems and nonlinear singularity formation)
  • Shock waves (their formation, structure and dynamics)

Dr Haiyan Zheng

Research Interests:

  • Adaptive designs in clinical trials
  • Bayesian data augmentation
  • Finite mixture distributions

Haiyan is interested in the design and analysis of clinical trials, particularly in the field of precision medicine. Her research is directed towards added efficiency of trials. This includes (1) leveraging historical data, (2) permitting mid-course adaptations, (3) simultaneous evaluation of multiple treatments, multiple subgroups, or both, under one overarching protocol, (4) enrichment strategies, etc.

Haiyan’s work has wider applications going beyond clinical trials. For instance, a few Bayesian methods developed to deal with a prior-data conflict can be applied broadly to augment studies or experiments suffering from data sparsity with external information.

 

LINKS:

Haiyan Zheng on University of Bath Research Portal

Dr Jennifer Tweedy, Daphne Jackson Royal Society Research Fellow

Research interests:

  • Mathematical medicine
  • Fluid mechanics
  • Mathematical modelling

Jennifer’s research involves modelling real life physiological and pathological conditions to understand physiology in health and disease, as well as the effect of potential or actual treatments. Most of her current research is in the mechanics of the eye, including the flow of the aqueous and vitreous humours that fill the chambers of the eye and the flow of fluid in and around the blood vessels at the back of the eye. Her research involves modelling, simplifying and idealising, and solving problems using a variety of techniques, both analytical and numerical.

 

LINKS:

Jennifer Tweedy on the University of Bath Research Portal

Dr Thomas Burnett

Research interests:

Tom’s research interest is in medical statistics, with a particular focus on the design and analysis of adaptive clinical trials. While his work is primarily methodological in nature, he collaborates closely with the pharmaceutical industry to ensure the methods are well matched with practice. Such methods have broader potential application as experimental designs, for example in the wider context of personalised healthcare.

 

LINKS:

Thomas Burnett on the University of Bath Research Portal

Dr Vangelis Evangelou

Research interests:

  • Generalised Linear Models: Modelling, Approximate Methods, Value of Information
  • Spatial and Spatial-Temporal Geostatistics: Modelling, Sampling Design
  • Time Series: Modelling, Sequential Analysis

Vangelis’s research interests are in the area of geostatistics, the collection and analysis of spatial data. He works on developing complex spatial models and methods for fitting these models to data and in spatial network design and spatial data collection. He develops design criteria and algorithms that can be used for general spatial models with applications in environmental data, analysis of human diseases, and agricultural studies.

 

LINKS:

Vangelis Evangelou on the University of Bath Research Portal