Nikita Nikolaev

PhD Candidate
Department of Mathematics
University of Toronto

Contact Information

Nikita Nikolaev
[nɪ.kɘ.'lɑ:.jev]
nikolaev at math dot utoronto dot ca
1-416-978-2095
1-416-978-4107     (attn: N. Nikolaev)
Department for Mathematics
University of Toronto
Bahen Centre

40 St. George Street
Toronto, Ontario
Canada, M5S 2E4

Research Interests

Broadly speaking, my research area is Complex Algebraic Geometry with its relevance to Quantum Field Theory and String Theory.

More specifically, my research revolves around the study of the moduli space of meromorphic flat connections using methods from the theory of Higgs bundles developed by Nigel Hitchin.

Currently, I'm working on a project in close collaboration with Alberto García Raboso and my advisor Marco Gualtieri.

PhD
advisor
MMath
advisor
Broad Keywords:
algebraic geometry
complex geometry
algebraic analysis
mathematical physics
string theory
Specific Keywords:
Lie algebroids and Lie groupoids
moduli spaces of Higgs Bundles
moduli spaces of meromorphic connections
spectral correspondence
spectral networks
wall-crossing
exact WKB
topological recursion
quantum curves

Notes

Lecture Notes

Notes taken in the Homotopical Structures Seminar.
homotopical algebra
operad
These are lecture notes for the course on D-modules that I took some years ago, read by Sergey Arkhipov.
D-modules
meromorphic connections
Riemann-Hilbert correspondence

Slides

8 December, 2014
Recent works of Gaiotto, Moore, and Neitzke introduced a tool, consisting of objects called Spectral Networks, to compute certain invariants in quantum field theory. I will describe how these objects are constructed and their relation to the moduli spaces of flat connections.
Spectral networks
moduli space of flat connections