Damián Gvirtz-Chen
About
I am a Lecturer (equivalent to a U.S. Assistant Professor) in Pure Mathematics at the University of Glasgow.
Contact
damian[insert a dot here]gvirtz@glasgow.ac.uk
Room 209B
School of Mathematics and Statistics
University of Glasgow
University Place
Glasgow G12 8QQ
United Kingdom
Tel: 01413302981
Research
I work at the intersection of algebraic geometry and number theory on the behaviour of rational points on algebraic varieties. My past research interests have included K3 surfaces, zero-cycles, Brauer-Manin obstruction, density of rational points, the Hilbert Property and p-adic geometry.
Publications and preprints
Past papers of mine have appeared under the author name Damián Gvirtz.
-
Hilbert modular surfaces with the Hilbert property
(with Julian Demeio)
in preparation. -
Non-thin rational points for elliptic K3 surfaces
(with Giacomo Mezzedimi)
11 pages, submitted. -
Surfaces defined by pairs of polynomials
(with Alexei N. Skorobogatov)
31 pages, submitted. -
Rational curves and the Hilbert Property on Jacobian Kummer varieties
(with Zhizhong Huang)
15 pages, submitted. -
A Hilbert Irreducibility Theorem for Enriques surfaces
(with Giacomo Mezzedimi)
24 pages, Transactions of the American Mathematical Society, Vol. 376 (2023). (arXiv) -
Cohomology and the Brauer groups of diagonal surfaces
(with Alexei N. Skorobogatov)
49 pages, Duke Mathematical Journal, Vol. 171, No. 6 (2022). (arXiv) -
Quantitative arithmetic of diagonal degree 2 K3 surfaces
(with Dan Loughran and Masahiro Nakahara)
75 pages, Mathematische Annalen (2021). (arXiv)
Typo alert: The q1 in Assumption 7.1(a) should read q0. -
Arithmetic Surjectivity for Zero-Cycles
25 pages, Mathematical Research Letters, Vol. 27, No. 5 (2020). (arXiv) -
Perfectoid Covers of Abelian Varieties
(with Clifford Blakestad, Ben Heuer, Daria Schedrina, Koji Shimizu, Peter Wear and Zijian Yao)
32 pages, Mathematical Research Letters, Vol. 29, No. 3 (2022). (arXiv) -
Topics in the arithmetic of hypersurfaces and K3 surfaces
PhD thesis, Imperial College, November 2019. -
Mazur’s Conjecture and an Unexpected Rational Curve on Kummer Surfaces and Their Superelliptic Generalisations
12 pages, Acta Arithmetica 187 (2019). (arXiv) -
Division algebras and maximal orders for given invariants
(with Gebhard Böckle)
17 pages, LMS Journal of Computation and Mathematics 19(A) (2016). -
On integral models of τ-sheaves for Drinfeld-Hayes modules in the elliptic
curve case
undergraduate research thesis, February 2014.
Conference organisation
PhD applicants
Teaching
Travel
A list of conferences and meetings where I have been/expect to be.
- Frontiers in Arithmetic Dynamics, 4th to 8th May 2024, BICMR
- Degree d points on algebraic surfaces, 18th to 22nd March 2024, AIM
- New Directions in Rational Points, 8th to 12th January 2024, Chennai Mathematical Institute
- Workshop on Arithmetic and Algebra of Rational Points, 11th to 15th September 2023, University of Bristol
- Specializations in Algebra and Number Theory, 26th to 29th June 2023, CMS Technion
- Arithmetic Geometry, Cryptography and Coding Theory, 5th to 9th June 2023, CIRM
- Arithmetic Statistics, 15th to 19th May 2023, CIRM
- Diophantine Geometry, 10th to 28th April 2023, MSRI
- The advent of rational points, 12th December 2023, KCL
- JNT Biennial Conference, 18th to 22nd July 2022, Cetraro
- ICM Number Theory and Geometry, 11th to 14th July 2022, ETH
- Rational Points on Higher-Dimensional Varieties, 25th to 29th April 2022, ICMS
- Rational Points Day, 9th November 2021, University of Bath
- Paris-London number theory seminar, 29th to 30th November 2021, Paris 13
- Skoro60bis, 3rd to 5th November 2021, IHP
- Arithmetic Statistics and Local-Global Principles, 20th to 24th September 2021, ESI
- Swinnerton-Dyer Memorial, 17th to 20th May 2021, Newton Institute
- Research Programme on Number Theory, Section on Rational Points, 29th March to 30th April 2021, IML
- Lean for the working mathematician, 13th to 17th July 2020, online
- Göttingen-Hannover number theory workshop, 22nd January 2020, Georg August University of Göttingen
- À la redécouverte des points rationnels - special trimester, 20th April to 12th July 2019, IHP
- À la redécouverte des points rationnels - preschool, 15th to 19th April 2019, CIRM
- Higher Dimensional Arithmetic Geometry, 18th to 21st February 2019, Kumamoto University
- Y-Rant, 8th to 9th November 2018, University of Sheffield
- Rational Points on Schiermonnikoog, 2nd to 6th July 2018, Schiermonnikoog
- K3 surfaces and Galois representations, 2nd to 4th May 2018, Shepperton
- Autumn school: Topics in arithmetic and algebraic geometry, 9th to 13th October 2017, Johannes Gutenberg University Mainz
- Diophantine Problems, 11th to 15th September 2017, University of Manchester
- Arizona Winter School 2017, 11th to 15th March 2017, University of Arizona
- Perfectoid Spaces, 16th to 22nd Oct 2016, MFO
- Rational Points and Algebraic Geometry, 26th to 30th September 2016, CIRM
- Twelfth Algorithmic Number Theory Symposium, 29th August to 2nd September 2016, University of Kaiserslautern
- Fundamental Groups in Arithmetic Geometry, 26th May to 3rd June 2016, IHP
Short Biography
- since 2022: Lecturer in Pure Mathematics, University of Glasgow
- 2020-2022: Research fellow, University College London
- 2019-2020: Postdoctoral researcher, Leibniz University Hannover
- 2015-2019: PhD, Imperial College London
- 2011-2015: Undergraduate studies in Heidelberg and Cambridge
Other
A personal list of open questions.
In spring 2022, together with Chris Birkbeck and Luis Garcia I organised the London Number Theory Seminar at UCL.
In spring 2021, Andrew Graham and I organised the London Number Theory Study Group on the Bloch-Kato conjecture at UCL.
I co-founded and organised the London Junior Number Theory Seminar. Here is the old webpage.
A Horizontal Introduction to Algebraic Stacks: An expository essay I wrote on algebraic stacks a long time ago. None of the content is original but I have been told that it is a useful resource to learn the notorious subject.
Every week I sang with other mathematicians, mostly early music. If you live in the London area, maybe you would like join?
In my school years, I profited a lot from gifted education programmes and ever since, I have become involved in many of them myself as a mentor/tutor/teacher. Some of my favourites with the longest lasting impact are International Summer Science Institute, Life-Science Lab, Hector-Seminar, Deutsche SchülerAkademie, Science-Academy and Bundeswettbewerb Mathematik
Thank you to Lukas Kühne for letting me use his CSS rules.