Chris Nicholls

DPhil student in Number Theory, University of Oxford

I am a fourth year DPhil student at the University of Oxford working on rational points on higher genus curves under the supervision of Professor Victor Flynn. In particular, I study descent methods on Jacobians of higher genus curves. I also work on rational points on K3 surfaces. After attending the 2015 Arizona Winter School, I have collaborated with Florian Bouyer, Edgar Costa, Dino Festi and Mckenzie West on a project to determine the Galois module structure of the Picard lattice of a family of K3 surfaces.

Research

Papers

An explicit embedding of the Kummer variety of genus three superelliptic curves (in preparation).
On the arithmetic of a family of degree two diagonal K3 surfaces, with F. Bouyer, E. Costa, D. Festi, M. West (arXiv, Math. Proc. Camb. Philos. Soc.).

Notes and Talks

Junior number theory talks

These are talks that I have given at the Oxford Junior Number Theory Seminar.
Large rational torsion
High descent on jacobians of curves

Abelian varieties study group

I organised a study group in abelian varieties in 2016. Here are three of my talks from that.
Basic definitions
Theorem of the cube
Dividing varieties by finite groups

CNTA Poster 2016

I gave a poster at the 2016 CNTA conference.
An explicit embedding of the Kummer variety of genus three superelliptic curves

YRM 2015

A talk I gave at the 2015 YRM (Young Researcher's in Mathematics) conference.
Descent methods on jacobians of higher genus curves

Galois Podcast

I also appeared on an 'In Our Spare Time' podcast about Galois theory: Evariste Galois

Code

Machine Learning

I am also interested in machine learning, and have done two internships at MathWorks in the machine learning group, working on convolutional neural networks. In my spare time I have worked on deep reinforcement learning.
My github site
My github blog
A talk I gave at a graduate reading group in machine learning (aimed at a non-technical audience): An Introduction to Machine Learning and Neural Networks

Contact

Address

Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG