# Florian Bouyer (DO NOT DELETE)

Having finished my PhD at Warwick, this page will no longer be accessible to me. The links to the lecture notes will still be available, but please go to https://sites.google.com/site/fjscbouyer/ for an up to date website and information.

I am a final year PhD student in Number Theory and Algebraic Geometry. I am working under the supervision of Damiano Testa. I'm currently studying K3 surfaces, in particular looking at Picard numbers, conics (particularly their fields of definitions and monodromy group) on certain K3 surfaces with a sympletic $\left(\mathbb{Z}/2\mathbb{Z}\right)^4$ action.

Email: F.bouyer@(usual Warwick ending)

Office: MS.B2.01

On it you can find talks I have given and teaching I have done (and more formally my CV, updated 06/11/2015)

Publications and Preprints

The Picard Group of Various Families of $\left(\mathbb{Z}/2\mathbb{Z}\right)^4$-invariant Quartic K3 Surfaces;
Preprint: arXiv 1511.01781
On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 Surfaces;
Preprint: arXiv 1511.01299
Examples of CM curves of genus two defined over the reflex field, with Marco Streng.
LMS Journal of Computation and Mathematics, Vol. 18 (2015), issue 01, pp 507-538. Journal and arXiv (Extra resources)

1st Year PhD Report

This is the report I did for my first year of PhD. It gives a brief background to K3 surfaces and Picard groups. This is followed by a discussion on different methods to find the Picard rank of K3 surfaces, before applying the theory to a specific family of K3 surfaces.

Finding the Picard Rank of a Certain Family of K3 Surfaces

4th Year Project

This is the essay I did during my fourth year MMath degree at Warwick. It is on Binary Quadratic Forms, Gauss Composition and Bhargava's Cube. It starts with a quick recap on Gauss composition before covering in details, with example, Bhargava's cube as discuss by Manjul Bhargava's 2004 paper on Higher Composition Laws I.

Composition and Bhargava's Cubes

Lecture Notes and Study Groups Notes

These are various lecture and study groups notes that I have typed up while attending courses at Warwick (or conferences elsewhere). They have not been thoroughly checked and might still contains typos and errors. Feel free to download them for your personal use but do not solely rely on them for your exams, especially if the notes are not from your year, courses can (and will) change from year to year. Please email me any corrections that needs to be made.

Due to popular request, I am also including both a TeX and LyX file of most set of notes which are complete under the GNU licence . If you have never used Tex or want to learn to use TeX with a more WYSIWYM I strongly encourage you to check out Lyx

by no mean