# 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 action.

**Email: **F.bouyer@(usual Warwick ending)

**Office: **MS.B2.01

**Website: **https://sites.google.com/site/fjscbouyer/

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 -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

- Algebraic Geometry (from the 2011-2012 course): TeX, LyX.
- Algebraic Geometry 2 (from the 2014-2015 course)
- Algebraic Groups (Study Group Autumn 2014)
- Algebraic Number Theory (from the 2010-2011 course): TeX, LyX.
- Algebraic Number Theory 2 (from the 2014-2015 TCC course)
- Commutative Algebra (from the 2011-2012 course, references to commutative algebra in Ring Theory refer to these notes): TeX, LyX.
- Commutative Algebra II (from the 2012-2013 course): TeX.
- Euler Systems (Study Group Summer 2015)
- Galois Representations (Study group Autumn 2014)
- Graduate Algebra (from the 2012-2013 course): TeX, LyX.
- Introduction to Hodge Theory and K3 surfaces (based on a Master Class in Strasbourg 2013).
- Intersection Theory (Study Group Autumn 2014)
- Local Fields (from the TCC 2013-2014 course): TeX, LyX.
- Modular Curves (from the TCC 2013-2014 course) TeX, LyX.
- Modular Representation (Study Group Summer 2015)
- Presentation of Groups (from the 2012-2013 course): TeX, LyX.
- Quadratic Forms (from the 2011-2012 course): TeX, LyX.
- Representation Theory (from the 2013-2014 course): TeX, LyX.
- Ring Theory (from the 2012-2013 course): TeX, LyX.
- Schottky groups and Mumford curves (Study Group Summer 2014)