Rob de Jeu

Contact Information

Faculteit der Bètawetenschappen
Afdeling Wiskunde
Vrije Universiteit
De Boelelaan 1111
1081 HV Amsterdam
The Netherlands

Office: 9A-27, NU building
Telephone: +31-20-598 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 K-theory, especially in the direction of Zagier's, Goncharov's and Beilinson's conjectures. It involves making K-groups more explicit, computing regulators and establishing relations between those regulators and the values of L-functions 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 K-theory. 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 K-Theory, 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 EC-funded Arithmetic Algebraic Geometry network, or through other sources of money (including EPSRC (UK) and NWO (The Netherlands), I had various postdocs, including Jean-Guillaume 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 K-theory, 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, 19th-23rd 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, 7th-12th December 2014) together with Pedro Luis del Angel, Javier Elizondo, James Lewis, Paulo Lima-Filho and Deepam Patel.

Preprints and abstracts of publications

Zagier's conjecture and wedge complexes in algebraic K-theory, Compositio Mathematica, 96 (1995), 197-247.
On K₄⁽³⁾ of curves over number fields, Inventiones Mathematicae, 125 (1996), 523-556.
A counterexample to a conjecture of Beilinson, The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 491-493, NATO Science Series C Mathematical and Physical Sciences, 548, Kluwer Academic Publishers, Dordrecht, 2000.
Towards regulator formulae for the K-theory of curves over number fields, Compositio Mathematica, 124 (2000), no. 2, 137-194.
A remark on the rank conjecture, K-theory, 25 (2002), no. 3, 215-231. Erratum.
The syntomic regulator for the K-theory of fields (with Amnon Besser), Annales Scientifiques de l'École Normale Supérieure, 36 (2003), issue 6, 867-924.
Numerical verification of Beilinson's conjecture for K₂ of hyperelliptic curves (with Tim Dokchitser and Don Zagier), Compositio Mathematica, 142 (2006), issue 2, 339-373.
Li^(p)-service? An algorithm for computing p-adic polylogarithms (with Amnon Besser), Mathematics of Computation, 77 (2008), 1105-1134. 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 K-theory, 1 (2008), issue 1, 169-173.
On the p-adic Beilinson conjecture for number fields (with Amnon Besser, Paul Buckingham and Xavier- François Roblot), Pure and Applied Math Quarterly, 5 (2009), number 1, 375-434 (special issue in honor of Jean-Pierre 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 K-theory and the Lichtenbaum-Gross conjecture (with David Burns and Herbert Gangl), Advances in Mathematics, 230 (2012), issue 3, 1502-1529.
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 K₄ of curves (with Amnon Besser), Pacific Journal of Mathematics, 260 (2012), number 2, 305-380 (special issue in memory of Jon Rogawski).
Beilinson's Hodge conjecture for smooth varieties (with James Lewis), Journal of K-theory, 11 (2013), issue 2, 243-282.
On K₂ of certain families of curves (with Hang Liu), International Mathematics Research Notices, 2015 (2015), issue 21, 10929-10958.
Étale cohomology, cofinite generation, and p-adic L-functions (with Tejaswi Navilarekallu), Annales de l'Institut Fourier, 65 (2015), numéro 6, 2331-2383.
A relative version of the Beilinson-Hodge conjecture, (with James Lewis and Deepam Patel) Recent advances in Hodge theory (period domains, algebraic cycles, and arithmetic), 241-263, London Mathematical Society Lecture Note Series, 247, Cambridge University Press, 2016.
Hyperbolic tessellations and generators of K₃ for imaginary quadratic fields (with David Burns, Herbert Gangl, Alexander D. Rahm and Dan Yasaki), Forum of Mathematics, Sigma, 9 (2021).
K₂ of families of elliptic curves over non-Abelian 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 p-adic Artin L-functions (with Xavier-François 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. (Note: You or your institution must have a valid MathSciNet subscription for this to work.)