**algebraic geometry**, which studies shapes that can be described by polynomials. I am particularly interested in the links of this theory to concepts in theoretical physics such as string theory.

Good

morning!

Hi! My name is **Aporva Varshney**, 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**,
inspired by theoretical physics.
I am also an avid programmer, having studied **joint mathematics and computer science** for my
undergraduate degree at Imperial College London. Additionally, I spent my summers
working at **Bloomberg** and **Meta** as a software engineering intern.

E-mail: `varshney dot aporva at gmail dot com`

Education

2022-

PhD Sudent in Mathematics

University College London

My research focuses on a branch of mathematics known as **algebraic geometry**,
which studies shapes that can be described by polynomials.
I am particularly interested in the links of this theory to concepts in theoretical
physics such as string theory.

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 - specifically,
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

During my 12 week placement, 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.**

Maths!

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.

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.

This Website!

Personal Project, 2022

A website and blog written without any frameworks, boilerplate code or
static site generators, and < 20 lines of Javascript.