Damián Gvirtz-Chen
About
I am a Lecturer (roughly equivalent to U.S. Assistant Professor) in Pure Mathematics at the University of Glasgow. My current research is supported by an EPSRC New Investigator Award.
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.
-
Galois Realisations of PSL2(p^2) via non-unirational Hilbert Irreducibility
(with Julian Demeio)
31 pages. -
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, Journal of the European Mathematical Society (2025). (arXiv) -
Rational curves and the Hilbert Property on Jacobian Kummer varieties
(with Zhizhong Huang)
16 pages, to appear in Algebra and Number Theory. -
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.
Recent organisation
Scottish Border Workshop in Dryburgh Abbey, December 2026
Rational Points in Glasgow, May 2024
PhD applicants
Current supervisions
- Lewis Bushen
- Ruth Raistrick
- Alistair Severn
- James Rawson
Teaching
Travel
A list of conferences and meetings where I have been/expect to be.
- Birational Geometry and Number Theory, 28th October to 1st November 2024, ICMS
- 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.