My research focuses on a branch of mathematics known as algebraic geometry,
which studies shapes that can be described by polynomials. I study an associated structure
known as the derived category, which captures a lot of information about these shapes.
For experts, I work on using the machinery of geometric invariant theory to find derived autoequivalences
for flopping varieties, or establishing semiorthogonal decompositions.
Good
morning!
Hi! My name is Aporva Varshney (pronounced with a silent 'a', as in 'Aporv')
and I'm a PhD student in mathematics at University College London,
aligned with the London School of Geometry and Number Theory. I study algebraic geometry,
supervised by Professor Ed Segal.
I studied joint mathematics and computer science for my
undergraduate degree at Imperial College London and spent my summers
working at Bloomberg and Meta as a software engineering intern.
My research is in algebraic geometry, a field which studies systems of polynomial equations and
seeks to understand properties of the shapes described by the solutions.
My work interacts with wider questions about possible classifications of these shapes.
E-mail: aporva dot varshney dot 22 at ucl dot ac dot uk
Maths!
Derived autoequivalences of length 2 flops via GIT
Preprint, 2025
This work studies the universal length 2 flop and constructs
the associated stringy Kähler moduli space (SKMS).
This unifies two approaches to building the conjectural SKMS in this setting.
Categorical absorption of a non-isolated singularity
To appear in 'Journal of Non-Commutative Geometry'
This paper studies a non-isolated threefold singularity, representing it
at the level of the derived category through an absorbing algebra.
The behaviour under resolutions and smoothings is considered.
The Geometry of Berkovich Analytic Spaces
Master's Thesis, 2022
Berkovich spaces are a type of analytic space over non-Archimedean fields.
This project looked at various techniques to determine aspects of their structure -
in particular, the notion of a skeleton.
Classification of compact analytic manifolds over non-Archimedean locally compact fields
Summer Research Project, 2021
I studied the classification theorem for compact analytic manifolds over the p-adics, and
completed Serre's proof-sketch into a full proof, using only direct methods from topology
and non-Archimedean analysis.
Education
2022-
PhD Sudent in Mathematics
University College London
2018-2022
MEng Mathematics and Computer Science
Imperial College London
I graduated with first class honours.
My final year thesis was on non-Archimedean geometry,
studying the notion of Berkovich spaces.
Employment
June - September 2021
Software Engineering Intern
Meta
As part of the data retention team, I created software to
detect and delete inaccessible user data in the
company databases. I enhanced the team's existing deletion pipelines
to support automatic deletion of entire columns in a database. As this was a
critical operation, I designed safeguards to minimise risk of
deleting in-use data.
July - September 2020
Software Engineering Intern
Bloomberg
I worked in a backend team which managed virtual machines used by developers across the company.
Spikes in the loads on specific servers frequently lead to delays and downtime in the
services provided by the team, and previously required manual intervention.
I developed an algorithm and various heuristics
to rebalance the resource usage.
Programming Projects
Grenade
University Project, 2021
A group project centered on developing a neural network library
for Haskell, using dependent types to catch errors at compile time.
APE2D Game Engine
Personal Project, 2018
A 2D game engine developed for modern C++, following a data-oriented philosophy by
using an entity-component-system architecture.
Website Design