## 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