Aporva's Website

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.

E-mail: aporva dot varshney dot 22 at ucl dot ac dot uk

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. Specifically, I study an algebraic structure associated to these shapes known as the derived category. I am particularly interested in connections with theoretical physics.

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.

Maths!

Categorical absorption of a non-isolated singularity

This pre-print 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.

Programming Projects

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

Made for the online DOGs seminar, featuring an appropriate amount of dogs.

Maths Tutoring Website

Website made for a client to advertise maths tutoring services.

KCL/UCL Junior Geometry

Designed for the junior geometry seminar at UCL with custom graphics.