David Holmes

Assistant professor at the University of Leiden

Office: Snellius gebouw 233
Niels Bohrweg 1
2333 CA Leiden
The Netherlands
E-Mail: 2...@gmail.com
curriculum vitae

Mail address:
Mathematisch Instituut
Postbus 9512
2300 RA Leiden
Tel : +31 71 5277133


Spring 2017, second half: Linear algebra 2. More information here.

Notes for lecture 4 of the intensive course on cats and mods are here.

Autumn 2016, second half: Linear algebra 1. More information here.

Autumn 2016: Mastermath Algebraic Geometry (with Robin de Jong). More information here

Information on previous courses here

PhD students

Garnet Akeyr

Raymond van Bommel (co-supervised with Fabien Pazuki)

Giulio Orecchia (co-supervised with Jilong Tong)

Masters students

Martin Heemskerk, studying derived categories of sheaves.

Arend de Jonge, working on minimal desingularisations of aligned nodal curves.

Raymond van Bommel (thesis `Almost all hyperelliptic Jacobians have a semi-abelian prime ', graduated summer 2014)

Erik Visse (with Rachel Newton, thesis `Local computations on the Cassels-Tate pairing on an elliptic curve', see also arXiv preprint, graduated spring 2014)

Michele Serra (thesis `Smooth models of curves', graduated summer 2013)

Publications/to appear

(with José Burgos Gil and Robin de Jong) `Positivity of the height jump divisor', to appear in IMRN - [arXiv]

(with Owen Biesel and Robin de Jong) `Néron models and the height jump divisor', to appear in Transactions of the AMS - [arXiv]

`Néron models of jacobians over base schemes of dimension greater than 1', to appear in Journal für die reine und angewandte Mathematik - [journal | arXiv]

`Quasi-compactness of Néron models, and an application to torsion points', Manuscripta Math. (2016) - [journal | arXiv]

(with Réne Pannekoek) `The Brauer-Manin obstruction on Kummer varieties and ranks of twists of abelian varieties', Bulletin of the London Mathematical Society (2015) - [journal | arXiv]

(with Robin de Jong) `Asymptotics of the Néron height pairing', Math. Res. Lett. (2015) - [journal | arxiv]

`An Arakelov-Theoretic approach to naive heights on hyperelliptic Jacobians', New York J. Math. (2014) - [journal | arXiv ]

`Computing Néron-Tate heights of points on hyperelliptic Jacobians', J. Number Theory (2012) - [ journal | arXiv]

Submitted articles

`Extending the double ramification cycle by resolving the Abel-Jacobi map' - [arXiv]

(with Owen Biesel) `Fine compactified moduli of enriched structures on stable curves' (submitted) - [arXiv]

`Torsion points and height jumping in higher-dimensional families of abelian varieties' (submitted) - [arXiv]

(with José Burgos Gil and Robin de Jong) `Singularity of the biextension metric for families of abelian varieties' (submitted) - [arXiv]

`A Néron model of the universal jacobian' (submitted) - [arXiv]


`Néron-Tate heights on the Jacobians of high-genus hyperelliptic curves', PhD thesis (2012) - [submitted version]

`Fibrations', essay for part III in Cambridge (2008) - [submitted version]

Not intended for publication

`When blowups are flat' - [pdf]

`A note on Néron models, heights and torsion points' (this is now superseded (and corrected)) by `Quasi-compactness of Néron models, and an application to torsion points' and `Torsion points and height jumping in higher-dimensional families of abelian varieties') - [pdf]

(with Réne Pannekoek) `Distributions of rational points on Kummer Varieties' - [arXiv]

Notes and slides from some of my talks

Notes for a talk on valuativisations at Garnet Akeyr's log geometry seminar. First talk reached end of 2.5.3.

Notes from bachelor seminar talk on `Counting rational curves in the plane' at Leiden (May 2017).

Slides from contributed talk on `A Néron model of the universal Jacobian' at the 2015 Summer Research Institute on Algebraic Geometry, Utah (July 2015). The talk also included some parts on the whiteboard, which are similar to things in various talks below.

Notes from colloquium talk on `complexity of rational solutions to polynomial equations' at the Universiteit van Amsterdam (February 2015).

Notes from a talk on the Neron models of jacobians over higher-dimensional bases at the Leiden algebra seminar (February 2015).

Notes from a talk on the Neron models of the universal jacobian (and some arithmetic applications) at the Utrecht `Geometry and Algebra, Geometry and Analysis' seminar (January 2015).

Notes from a talk on Neron models in higher dimension at the ARIVAF closing conference in Bordeaux (Autumn 2014).

Notes from a talk on Neron models in higher dimension at the ICMAT in Madrid for the research trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory (Autumn 2014).

Hamburg number theory seminar talk explaining part of my PhD thesis (summer 2012).

Basic talk on the universal elliptic curve given to Hamburg undergraduates (spring 2012).

Equations for a genus 2 Jacobian- often useful/fun.

Typed notes for a talk on `Compactifications of Siegel Modular Varieties' for the `Moduli of Abelian Varieties Seminar (08/02/2012).

Slides for a talk `Functional Equations' for the joint Warwick-Bristol Langlands programme reading group (summer 2011).

Scanned notes for an introductory talk for the Neron models reading group

Other things

Some fun pictures coming from universal Néron model admitting stacks - feel free to ask for more details...

Sage worksheet for automatically generating questions for linear algebra exams (eg. `random' matrices in GL_n(Z) with small entries).

A page with some information relating to recent talk at Skinner's school.

Notes from talks by Angelo Vistoli at the summer school on Stacks, Mainz, 2015.

Notes from a course I taught on elliptic curves in Leiden. Many thanks to Steve Alberts for typesetting.

Page on pronouns for students writing theses.

Eclipse photos 2015