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 . From October 2022 until August 2024, I was a 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!
Invited talk
Invited talk
Participation in conference - Academic
Invited talk
Participation in workshop, seminar, course
- Combinatorics
- Probability