Hola! I am a third year PhD student in algebraic geometry and number theory under the supervision of Professor Gavin Brown and Dr Damiano TestaLink opens in a new window. Some of the topics that I am currently interested in are: K3 surfaces and their arithmetic, singularities in positive characteristic, and how to use explicit models of Kummer varieties for studying rational points on curves. Here is my GitHubLink opens in a new window profile and here is my CVLink opens in a new window.

Education

I studied the MSc in Mathematical Sciences at the University of Oxford and the BSc in Mathematics at the Universidad de Salamanca (Spain). My master’s dissertation was about Local fields and the Hasse principleLink opens in a new window and was supervised by Prof. Victor FlynnLink opens in a new window. My bachelor’s degree final thesis was about Continued fractionsLink opens in a new window and was supervised by Prof. Luis M. Navas VicenteLink opens in a new window.

Talks

Research

• Masses of central leaves and automorphisms of Abelian varieties. Project in the Arizona Winter SchoolLink opens in a new window, joint with Enric Florit and Eda Kırımlı, 6th March 2024 (slidesLink opens in a new window).
• How to desingularise Kummer surfaces. Junior Geometry SeminarLink opens in a new window, King's College London / University College London, 26th February 2024 (slidesLink opens in a new window).
• Explicit theory of Kummer surfaces in characteristic two. Hodge ClubLink opens in a new window, University of Edinburgh, 9th February 2024 (slidesLink opens in a new window).
• Local normal forms of non-commutative potentials. RGAS School on SingularitiesLink opens in a new window, Instituto de Matemáticas de la Universidad de Sevilla, 11th January 2024 (slidesLink opens in a new window).
• Explicit theory of Kummer surfaces in characteristic two. Linfoot Number Theory SeminarLink opens in a new window, University of Bristol, 4th October 2023 (slidesLink opens in a new window).
• Crazy for two: Genus two curves in characteristic two via Kummer surfaces. Young Researchers in Algebraic Number Theory (Y-RANT)Link opens in a new window, 6^th September 2023 (slidesLink opens in a new window).
• Kummer surfaces: bridging the gap between geometry and number theory. Queer in Number Theory and Geometry (QuINGs)Link opens in a new window, 31^st August 2023 (slidesLink opens in a new window).
• A game-based learning intervention for support classes in Mathematics. Warwick Education Conference 2023: Empowering students and staff through small teachingLink opens in a new windotwLink opens in a new window, 19-21st June 2023 (videoLink opens in a new window).
• An arithmetic expedition into K3 surfaces. Warwick Junior Number Theory SeminarLink opens in a new window, 12^th June 2023.
• Explicit models of Kummer surfaces in characteristic two. 7th Symposium of the Roman Number Theory AssociationLink opens in a new window, 4^th May 2023 (slidesLink opens in a new window).
• An introduction to the Hasse principle through examples. Warwick Postgraduate Seminar, 19^th January 2022 (slidesLink opens in a new window).
• Picard-Fuchs equations in families of varieties. IMUS programme PI3: Introduction to Research, Universidad de Sevilla, 7^th September 2021.

Study groups and working seminars

• $\Gamma(n)$, $\Gamma_1(n)$ and $\Gamma_0(n)$-structures. Study group on moduli problems of elliptic curvesLink opens in a new window. 27^th October 2023 (notesLink opens in a new window).
• Rigidity and the construction of the dual abelian variety. Study group on abelian varieties.Link opens in a new window 17th October 2023 (notesLink opens in a new window).
• Classification of rational double points of surfaces in characteristic p (Artin's paperLink opens in a new window). 9^th June 2023.
• Characterisations of rational double points in surfaces. 26^th May 2023.
• Curves, surfaces and singularities in characteristic p. 19^th May 2023.
• The Eisenstein ideal. Study group on Mazur's torsion theorem, 7^th December 2022 (slidesLink opens in a new window).
• Hyperelliptic curves and their Jacobians. Study group on isogeny-based cryptographyLink opens in a new window, 2^nd December 2022 (slidesLink opens in a new window).
• An introduction to Grothendieck topologies. Study group on Grothendieck topologies and descentLink opens in a new window, 13^th October 2022.
• Intersection theory on surfaces. Study group on Hasse-Weil zeta functionsLink opens in a new window, 20^th May 2022 (slidesLink opens in a new window).
• Elliptic curves over discrete valuation rings. Study group on Mazur's torsion theorem, 25^th April 2022 (slidesLink opens in a new window).

Outreach

• Kissing in the 8^th dimension. XXIV National Meeting of Mathematics Students (ENEM), Universidad de Extremadura, 27^th July 2023.
• Braid theory applied to the design of friendship bracelets (workshop). XXIII National Meeting of Mathematics Students (ENEM), Universidad de Valencia, 27^th July 2022.
• Hold on tight! (Algebraic) curves are coming up! XXIII National Meeting of Mathematics Students (ENEM), Universidad de Valencia, 26^th July 2022.
• Very rational irrationals? Approximating with continued fractions. XXII National Meeting of Mathematics Students (ENEM), Universidad de Murcia, 28^th July 2021.
• Identification of symmetries and wallpaper groups in Nasrid tilings (workshop). XX National Meeting of Mathematics Students (ENEM), Universidad de Granada, 24^th July 2019.

Posters

• Presentations and 2-colourings of frieze groups. XX National Meeting of Mathematics Students (ENEM), Universidad de Granada.

Teaching

2023 - 2024

• Teaching assistant for MA397 - Consolidation.

2022 - 2023

• Teaching assistant for MA243 - Geometry.
• Teaching assistant for MA249 - Algebra II: Groups and Rings.
• Teaching assistant for MA448 - Hyperbolic Geometry (kahootsLink opens in a new window).

2021 - 2022

• Teaching assistant for MA2K3 - Consolidation.
• Teaching assistant for MA3D5 - Galois Theory (kahootsLink opens in a new window).
• Supervisor of one group of first-year undergraduate Mathematics students.

Contact

I am the co-organiser (together with James Rawson and Katerina Santicola) of Warwick's Junior Number Theory SeminarLink opens in a new window. If there is anything that I can help you with, you are more than welcome to send me an email to alvaro dot gonzalez-hernandez at warwick dot ac dot uk :)