Rob de Jeu
Contact Information
Faculteit der Bètawetenschappen
Afdeling Wiskunde
Vrije Universiteit
De Boelelaan 1111
1081 HV Amsterdam
The Netherlands
Office: 9A27, NU building
Telephone: +3120598 7676
Slides from talks
Here are
slides, etc., of some of my talks
(BMC 2001, BMC 2002, Dagstuhl 2004, Banff 2005, Belfast 2007, VU 2007, Utrecht
2009, Essen 2022, Paris 2023, ...).
Research Information
My work is concentrated around algebraic Ktheory, especially in the direction
of Zagier's, Goncharov's and Beilinson's conjectures. It
involves making Kgroups more explicit, computing regulators and
establishing relations between those regulators and the values of Lfunctions
at certain points.
Since this area relates to and uses techniques from
number theory and arithmetic algebraic geometry, I also do research
in those fields without any link to algebraic Ktheory. As some of my work is computer
based there are also algorithmic aspects to my research.
I was the scientist in charge of the Durham node in the EC network
Arithmetic Algebraic Geometry that ended
31st January 2008.
I was also associated with the Edinburgh node in the EC network
Algebraic KTheory, Linear Algebraic Groups and Related Structures,
which finished 30th September 2006.
Nowadays I take part in the
The Netherlands Organisation for Scientific Research (NWO)
clusters
DIAMANT
and
GQT.
Sander Dahmen,
Ilke Canakci
and (from September 2023)
Pol van Hoften
also work in my research group.
Through the ECfunded Arithmetic Algebraic Geometry network, or through other sources of money
(including EPSRC (UK) and NWO (The Netherlands), I had various postdocs,
including
JeanGuillaume Grebet, Niklas Broberg,
Ivan Horozov,
Daniel Caro,
Tejaswi Navilarekallu,
Marco Streng,
Deepam Patel,
and
Chun Yin Hui.
Hang Liu
visited me for the two years 2013 and 2014 while being a PhD student at the Graduate University of the Chinese Academy
of Sciences.
Events
We have a budding arithmetic seminar.
From time to time I have some
visitors.
With some other people I organized a
Stieltjes "onderwijsweek"
in January 2010, where the topics were inspired by
the
lectures of Spencer Bloch
as Stieltjes professor hosted by me in February and March 2010.
Together with
Aravind Asok,
Charles Doran,
Roy Joshua,
Marc Levine,
James D. Lewis and
Ursula Whitcher I ran
a semester on Ktheory, algebraic cycles, and motivic homotopy theory
at the Newton Institute in Cambridge, United Kingdom, in the
first half of 2020. Unfortunately this was cancelled from mid March 2020 onwards
due to the corona virus. The INI kindly allows us to
make up for the lost time
in May through July 2022.
Earlier I organized

a conference on algebraic cycles and motives
(Fields Institute, Toronto, 19th23rd March, 2007)
together with James D. Lewis,
which was dedicated to the mathematical heritage of
Spencer J. Bloch;

Regulators III in July 2010
in Barcelona,
together with José Burgos Gil, James Lewis, Joan Naranjo, Wayne Raskind
and Xavier Xarles;

a workshop on the cohomological realizations of motives
(BIRS, Banff, 7th12th December 2014) together with Pedro Luis del Angel, Javier Elizondo, James Lewis, Paulo
LimaFilho and Deepam Patel.
Preprints and abstracts of publications

Zagier's conjecture and wedge complexes in algebraic Ktheory,
Compositio Mathematica, 96 (1995), 197247.

On K_{4}^{(3)} of curves over number fields,
Inventiones Mathematicae, 125 (1996), 523556.

A counterexample to a conjecture of Beilinson,
The arithmetic and geometry of algebraic cycles (Banff, AB, 1998),
491493, NATO Science Series C Mathematical and Physical Sciences, 548, Kluwer Academic Publishers, Dordrecht, 2000.

Towards regulator formulae for the Ktheory of curves over number fields,
Compositio Mathematica, 124 (2000), no. 2, 137194.

A remark on the rank conjecture,
Ktheory, 25 (2002), no. 3, 215231.
Erratum.

The syntomic regulator for the Ktheory of fields
(with Amnon Besser), Annales Scientifiques de l'École Normale Supérieure, 36 (2003), issue 6, 867924.

Numerical verification of Beilinson's conjecture for K_{2} of hyperelliptic curves
(with Tim Dokchitser and Don Zagier), Compositio Mathematica, 142 (2006), issue 2, 339373.

Li^{(p)}service? An algorithm for computing padic polylogarithms
(with Amnon Besser), Mathematics of Computation, 77 (2008), 11051134.
The latex versions of the tables in the paper were created by reading this
input data
into the Magma programs corresponding to
table 1,
table 2,
table 3
and
table 4.

Further counterexamples to a conjecture of Beilinson,
Journal of Ktheory, 1 (2008), issue 1, 169173.

On the padic Beilinson conjecture for number fields
(with Amnon Besser, Paul Buckingham and Xavier François Roblot),
Pure and Applied Math Quarterly, 5 (2009), number 1, 375434
(special issue in honor of JeanPierre Serre).

Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch
(Rob de Jeu, James D. Lewis, Editors).
Fields Institute Communications, vol. 56,
AMS (Providence, R.I.)/Fields Institute (Toronto, Ontario), 2009.

On special elements in higher algebraic Ktheory and the LichtenbaumGross conjecture
(with David Burns and Herbert Gangl),
Advances in Mathematics, 230 (2012), issue 3, 15021529.

Regulators
(José Burgos Gil, Rob de Jeu, James Lewis, Joan Naranjo, Wayne Raskind, Xavier Xarles, Editors).
Contemporary Mathematics, vol. 571, AMS (Providence, R.I.), 2012.

The syntomic regulator for K_{4} of curves
(with Amnon Besser),
Pacific Journal of Mathematics, 260 (2012), number 2, 305380
(special issue in memory of Jon Rogawski).

Beilinson's Hodge conjecture for smooth varieties
(with James Lewis),
Journal of Ktheory, 11 (2013), issue 2, 243282.

On K_{2} of certain families of curves
(with Hang Liu),
International Mathematics Research Notices, 2015 (2015), issue 21, 1092910958.

Étale cohomology, cofinite generation, and padic Lfunctions
(with Tejaswi Navilarekallu),
Annales de l'Institut Fourier, 65 (2015), numéro 6, 23312383.

A relative version of the BeilinsonHodge conjecture,
(with James Lewis and Deepam Patel)
Recent advances in Hodge theory (period domains, algebraic cycles, and arithmetic),
241263, London Mathematical Society Lecture Note Series, 247, Cambridge University Press, 2016.

Hyperbolic tessellations and generators of K_{3} for imaginary quadratic fields
(with David Burns, Herbert Gangl, Alexander D. Rahm and Dan Yasaki),
Forum of Mathematics, Sigma, 9 (2021).

K_{2} of families of elliptic curves over nonAbelian cubic and quartic fields
(with François Brunault, Hang Liu and Fernando Rodriguez Villegas), submitted for publication.

Bounding generators for the kernel and cokernel of the tame symbol for curves, submitted for publication.

Conjectures, consequences, and numerical experiments for padic Artin Lfunctions
(with XavierFrançois Roblot), submitted for publication.

Frobenius lifts and point counting for smooth curves
(with Amnon Besser and François Escriva), preprint.

Describing all multivariable functional equations of dilogarithms,
preprint.
Click
here
to get a listing of my papers from AMS MathSciNet.
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