David Holmes
I have not moved, but my webpage has: new page at davidholmes.nl.
This page will remain here for the moment, so as to avoid breaking links. But I am not planning to keep it updated (because connecting to the university servers is getting too painful).
Associate professor at the University of Leiden
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Office: Snellius gebouw 233 |
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Teaching
My courses are generally on Brightspace now, so I am not maintaining local webpages for most courses.
Notes for lecture 4 of the intensive course on cats and mods are here.
Information on previous courses here
PhD students
Graduated
Raymond van Bommel (co-supervised with Fabien Pazuki), now at MIT.
Giulio Orecchia (co-supervised with Qing Liu). Graduated February 2018. Beginning a postdoc at the IRMAR in Rennes in September 2018, soon moving to EPFL Lausanne.
Master's students
Giorgio Spadaccini, algebraic statistics
Sergej Monavari, Local picture of twisted curves
Rosa Schwarz, Gromov-Witten invariants of the classifying stack of principle Gm-bundles
Martin Heemskerk, Derived Categories of Projective Gorenstein Varieties
Arend de Jonge, 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 Owen Biesel) `Fine compactified moduli of enriched structures on stable curves', to appear in Memoirs of the AMS - [arXiv]
`The norm of the saturation of a binomial ideal, and applications to Markov bases', to appear in Algebraic Statistics - [arXiv]
(with Nick Rome) `Fields of definition of curves of a given degree', to appear in JTNB - [arXiv]
(with Aaron Pixton and Johannes Schmitt) `Multiplicativity of the double ramification cycle', Documenta - [journal|arXiv]
(with Martha Dellar, Kairsty Topp, Guillermo Pardo, Agustin del Prado, Nuala Fitton, Georgios Banos, and Eileen Wall), `Empirical and dynamic approaches for modelling the yield and N content of European grasslands', to appear in Environmental modelling and Software
`Extending the double ramification cycle by resolving the Abel-Jacobi map', to appear in JIM Jussieu - [arXiv]
`Torsion points and height jumping in higher-dimensional families of abelian varieties', to appear in IJNT - [arXiv]
(with Steffen Muller and Raymond van Bommel) `Explicit arithmetic intersection theory and computation of Neron-Tate heights', Mathematics of Computation - [journal|arXiv]
(with Jose Burgos Gil and Robin de Jong) `Singularity of the biextension metric for families of abelian varieties', Forum of Mathematics, Sigma - [journal|arXiv]
(with Jesse Kass and Nicola Pagani) `Extending the Double Ramification Cycle using Jacobians', European Journal of Mathematics (2018). doi - [journal|arXiv]
(with Jose Burgos Gil and Robin de Jong) `Positivity of the height jump divisor', IMRN (2017) - [journal|arXiv]
(with Owen Biesel and Robin de Jong) `Neron models and the height jump divisor', Trans. AMS 369 (2017), 8685--8723 - [journal|arXiv]
`Neron models of jacobians over base schemes of dimension greater than 1', Journal fur die reine und angewandte Mathematik - [journal | arXiv | video lecture]
`Quasi-compactness of Neron models, and an application to torsion points', Manuscripta Math. (2016) - [journal | arXiv]
(with Rene 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 Neron 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 Neron-Tate heights of points on hyperelliptic Jacobians', J. Number Theory (2012) - [ journal | arXiv]
Submitted articles
(with R. Schwarz) `Logarithmic intersections of double ramification cycles' - [arXiv]
(with G. Orecchia, S. Molcho and T. Poiret) `Models of Jacobians of curves' - [arXiv]
(with Y. Bae, R. Pandharipande, J. Schmitt, and R. Schwarz) `Pixton's formula and Abel-Jacobi theory on the Picard stack' - [arXiv]
(with Johannes Schmitt) `Infinitesimal structure of the pluricanonical double ramification locus' - [arXiv]
`A Neron model of the universal jacobian' - [arXiv]
Intended for submission
Theses
`Neron-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 Neron models, heights and torsion points' (this is now superseded (and corrected)) by `Quasi-compactness of Neron models, and an application to torsion points' and `Torsion points and height jumping in higher-dimensional families of abelian varieties') - [pdf]
(with Rene 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 Neron 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 Neron 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. 2019 Intercity geometry seminar on a preprint of Molcho and Wise in which they prove the representability (in a suitable sense) of the logarithmic Picard functor. I am organising this jointly with Chris Lazda, Adrien Sauvaget and Arne Smeets. See here for more information.