# 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

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.

Research

Area

Area

PhD

advisor

advisor

MMath

advisor

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

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

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

moduli space of flat connections

# Teaching

## Current Teaching

MAT136S

Integral Calculus

Spring 2017

lecturer

LEC5201

Thu 18-21

WB116

Thu 18-21

WB116

office hour: Tue 19-20 in BA6191