Nikita Nikolaev

Postdoctoral Research Associate

School of Mathematics and Statistics
University of Sheffield
United Kingdom

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Brief Profile

I am a mathematician, working as a postdoctoral research associate in the School of Mathematics and Statistics at the University of Sheffield. I am a member of the Algebraic Geometry and Mathematical Physics research group, where my mentor is Tom Bridgeland. My position is funded by the EPSRC programme grant Enhancing RNG, where my second mentor is Tudor Dimofte.

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Brief Research Profile

My research is broadly in geometry and mathematical physics. It lies at the interface of algebraic and differential geometry with strong connections to quantum field theory and string theory. I use a mix of mostly algebraic and to a lesser extent analytic techniques in order to solve problems, most of which are ultimately related to deep questions about singular differential equations.

More precisely, my work revolves around the study of the moduli spaces of flat meromorphic connections and Higgs bundles. Some keywords related to my research interests include (in no particular order): Stokes phenomenon, exact WKB analysis and exact perturbation theory, quantum curves, topological recursion, wall-crossing, cluster algebras, holomorphic Poisson structures, Riemann-Hilbert correspondence, Lie algebroids and groupoids.

  • Geometry and Mathematical Physics
  • Holomorphic Geometry
  • Complex Algebraic Geometry
  • Algebraic Analysis
  • Exact Perturbation Theory
  • Mathematical Physics

Brief Academic Bio

I got my undergraduate degree in Mathematics and Physics from the University of Toronto in Canada, where my unofficial senior-year mentor was Sergey Arkhipov. I then went to the University of Waterloo in Canada to get a master's degree in Pure Mathematics under the supervision of Ruxandra Moraru. My thesis title was Reduction Theory and Dirac Geometry.

I got my PhD in Mathematics from the University of Toronto in 2018 under the supervision of Marco Gualtieri. My PhD thesis title was Abelianisation of Logarithmic Connections. I am a second-generation mathematical descendant of Nigel Hitchin.

I then held a 3-year postdoc position at the University of Geneva in Switzerland with Anton Alekseev. In March 2021, I joined the University of Sheffield in the UK as a postdoc with Tom Bridgeland.

In September 2022, I will join the University of Birmingham as a Marie Skłodowska-Curie Fellow, hosted and mentored by Marta Mazzocco.

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