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Nicholas Fleming Vázquez

Mathematician on a hikeI recently completed my PhD under the supervision of Professor Ian Melbourne. I am now a postdoc at the University of Toronto.

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).


  • Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-mixing Nonuniformly Hyperbolic Maps, Communications in Mathematical Physics, 2022 [arxiv, journal]
  • Functional Correlation Bounds and Deterministic Homogenisation of Fast-slow Systems, preprint, 2023 [arxiv]


  • 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
  • Deterministic homogenisation of fast-slow systems and functional correlation bounds, Lorentz Gas conference (Leiden, Netherlands), 22nd December 2022


I have previously been a TA for Norms, Metrics and Topologies (twice), Mathematical Analysis III and Ergodic Theory. 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