I'm a final year PhD student under the supervision of Professor Ian Melbourne. I completed an MMath at the University of Warwick in 2019, where my final year project was also supervised by Ian.
I am broadly interested in Ergodic Theory and Probability. In particular, I am interested in statistical properties of nonuniformly hyperbolic dynamical systems. Most of my research so far has been related to proving averaging/homogenisation for deterministic dynamical systems (here is a nice survey article on deterministic homogenisation).
- Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-mixing Nonuniformly Hyperbolic Maps, Communications in Mathematical Physics, 2022 [arxiv, journal]
- Homogenisation of Deterministic Fast-Slow Systems, Warwick Postgraduate Seminar (online), 18th November 2020
- Optimal iterated moment bounds for nonuniformly hyperbolic maps, Limit Theorems for Slowly Mixing Systems (Edinburgh, UK), 7th June 2022
- ____________, Warwick DAGGER Seminar, 27th June 2022
I have previously been a TA for Norms, Metrics and Topologies (twice) and Mathematical Analysis III. I also have experience supervising small groups of second-year maths students and first-year joint-honours students.
Email: n dot fleming dot 1 at warwick.ac.uk