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.

Research interests:

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).

Papers/preprints:

• Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-mixing Nonuniformly Hyperbolic Maps, Communications in Mathematical Physics, 2022 [arxiv, journal]

Talks:

• Homogenisation of Deterministic Fast-Slow Systems, Warwick Postgraduate Seminar (online), 18^th November 2020
• Optimal iterated moment bounds for nonuniformly hyperbolic maps, Limit Theorems for Slowly Mixing Systems (Edinburgh, UK), 7^th June 2022
• ____________, Warwick DAGGER Seminar, 27^th June 2022
• Deterministic homogenisation of fast-slow systems and functional correlation bounds, Lorentz Gas conference (Leiden, Netherlands), 22^nd December 2022

Teaching:

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