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Nikita Nikolaev

Postdoctoral Scholar
Section de Mathématiques
Université de Genève

Nikita Nikolaev

I am a Postdoctoral Scholar at the Section of Mathematics of the University of Geneva in Switzerland.
I am a member of the research group of Anton Alekseev.

I completed my PhD in Mathematics at the University of Toronto in January 2018.
My PhD advisor was Marco Gualtieri, and my thesis is titled Abelianisation of Logarithmic Connections.

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.

Research Area

Complex Algebraic Geometry
Mathematical Physics

Mentors

Research Group
Anton Alekseev

PhD Advisor
Marco Gualtieri

MMath Advisor
Ruxandra Moraru

Broad Keywords

algebraic geometry
complex geometry
algebraic analysis
mathematical physics
quantum field theory
string theory

Specific Keywords

Lie algebroids and Lie groupoids
Higgs bundles
meromorphic connections
spectral correspondence
spectral networks
wall-crossing
exact WKB analysis
topological recursion
quantum curves

Publications and Preprints

2 The Exact WKB Method is Abelianisation

Marco Gualtieri, Kohei Iwaki, Andrew Neitzke
in preparation
2018

1 Abelianisation of Logarithmic Connections

PhD Dissertation
2018
meromorphic connection, Levelt filtration, abelianisation, WKB, spectral curve, Higgs bundle, quantum connection, de Rham-Prym variety

Notes

2 Homotopical Structures

Notes taken in the Homotopical Structures Seminar.
2015
homotopical algebra, operad

1 Introduction to D-Modules

These are lecture notes for the course on D-modules that I took some years ago, read by Sergey Arkhipov.
2012
D-modules, meromorphic connections, Riemann-Hilbert correspondence

Talks and Travel

Forthcoming Events

2018

9-14 September
Workshop Geometry and Physics of Quantum Curves, BIRS, Banf, Alberta, Canada

16-20 July
Conference Poisson 2018, Fields Institute, Toronto, Ontario, Canada

29 May - 2 June
TBA (plenary talk)
Conference GAP XVI, West University of Timisoara, Romania

8-13 April
Conference Geometric aspects of momentum maps and integrability, CSF Ascona, Switzerland

March
TBA
Geometry Seminar, Radboud Universiteit Nijmegen, Netherlands

2 February
Geometry behind the WKB Method
Seminar Groupes de Lie et espaces des modules, Université de Genève, Switzerland

Recent Events

18 January
Abelianisation of Logarithmic Connections
Workshop Algebraic Structures in Topology and Geometry, Riederalp, Switzerland
Address
Office 202
Villa Battelle
Route de Drize 7
1227 Carouge
Switzerland
Contact Information
nikita.nikolaev@unige.ch
+41 22 379 00 82