Dr Jessica Jay
Lecturer in Security and Protection ScienceResearch Interests
My main area of research is Probability, in particular Interacting Particle Systems (IPS's). These are certain continuous time Markov processes on discrete state spaces with many applications, for example traffic/data flow, voting/opinion dynamics and also tumour growth.
Currently, I am interested in exploring links between IPS's and other areas of Pure Mathematics such as Combinatorics and Algebra. For example, comparing stationary measures for certain equivalent particle systems often leads to purely probabilistic proofs of both classic and new q-series identitites of combinatorial significiance (e.g. the Jacobi triple product identitiy).
I am also interested in applications of IPS's in the real world. If this is something you have ideas about then please feel free to get in touch!
Career Details
I was awarded my PhD in Mathematics from the Univeristy of Bristol in February 2023, under the supervision of Prof. Márton Balázs. From October 2022 until August 2024, I was a Heilbronn Research Fellow at the University of Bristol.
Web Links
Current Teaching
- MATH 332/432: Stochastic Processes
PhD Supervision Interests
I am interested in supervising PhD students who have a strong interest and background in discrete probability. My current research is in the theory of interacting particle systems. One potential project is to study the second class particle behaviour of certain reversible interacting particle systems. Interacting particle systems have been shown to have strong links to other areas of mathematics such as combinatorics (via partitions) and algebra (some systems can be constructed from certain quantum groups). I would be happy to discuss the potential for interested students to work on a jointly supervised project studying these links further. If you would like to know more, please feel free to get in touch!
77th British Mathematical Colloquium: Probability Section
Invited talk
Lancaster Probability Days
Participation in conference - Academic
Florence Nightingale Day 2026
Invited talk
London Mathematical Society Newsletter (Editorial Board) (External organisation)
Membership of board
Cyber Girls First Sixth Form event: Exhibition Hall
Festival/Exhibition/Concert
CyberFirst Days at Lancaster University
Types of Public engagement and outreach - Festival/Exhibition
University of Leicester Mathematics Seminar
Invited talk
LMS/IMA Joint Meeting 2025
Participation in conference - Academic
CyberFirst Days at Lancaster University
Types of Public engagement and outreach - Festival/Exhibition
Insight Summer School at Lancaster University - "My life in Mathematics" talk
Invited talk
The Magic of Maths
Public Lecture/ Debate/Seminar
Stochastics and Influences
Invited talk
Pint of Science
Participation in conference - Public
University of Bristol Probability Seminar
Invited talk
Probability, Analysis and Dynamics 2025
Participation in conference - Academic
Advances in Combinatorial and Algebraic Probability
Participation in workshop, seminar, course
Dualities in Probability and Algebra Workshop
Invited talk
- Combinatorics
- Probability