Prof. Dr. Jan Steffen Müller
Prof. Dr. Jan Steffen Müller

Jan Steffen Müller
Juniorprofessor
Carl von Ossietzky University Oldenburg
Institute for Mathematics
26111 Oldenburg
+49 441 798-3221
jan.steffen.mueller (at) uni-oldenburg.de
Office: Campus Oldenburg-Wechloy, Carl von Ossietzky Strasse, W1-1 106
RESEARCH INTERESTS
- Explicit methods in number theory
- Arithmetic geometry
PUBLICATIONS
- Computing integral points on hyperelliptic curves using quadratic Chabauty (with Jennifer Balakrishnan and Amnon Besser)
Math. Comp., published electronically: October 5, 2016, (to appear in print). [arxiv] - Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces (with Ulf Kühn),
Trans. Amer. Math. Soc. 369, 1869-1894 (2017). [arxiv] - Canonical Heights on Genus Two Jacobians (with Michael Stoll)
Algebra & Number Theory 10, 2153-2234 (2016). [arxiv] - Computing Canonical Heights on Elliptic Curves in Quasi-Linear Time (with Michael Stoll)
LMS J. Comput. Math. 19 (Special issue A – Algorithmic Number Theory Symposium XII), 391-405 (2016). [arxiv]. - Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves (with Jennifer Balakrishnan and Amnon Besser),
J. Reine Angew. Math. 720, 51-79 (2016). [arxiv] - A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties (with Jennifer Balakrishnan and William Stein),
Math. Comp. 85, 983-1016 (2016). [arxiv] - Rational points on Jacobians of hyperelliptic curves,
in L. Beshaj, T. Shaska, E. Zhupa (eds.): Advances on superelliptic curves and their applications, IOS Press, 2015. [pdf] - A height inequality for rational points on elliptic curves implied by the abc-conjecture (with Ulf Kühn),
Functiones et Approximatio Commentarii Mathematici, 52, 127-132 (2015). [pdf] [arXiv] - Canonical heights and division polynomials (with Robin de Jong),
Math. Proc. Camb. Phil. Soc. 157, 357-373 (2014). [pdf] [arxiv] [Magma-Code] - Explicit Kummer varieties of hyperelliptic Jacobian threefolds,
LMS J. Comput. Math. 17, 496-508 (2014). [pdf] [arxiv] [Magma-Code] - Computing canonical heights using arithmetic intersection theory,
Math. Comp. 83, 311-336 (2014). [pdf] [arXiv] - Local heights on elliptic curves and intersection multiplicities (with Vincenz Busch),
Int. J. Number Theory 8, No. 6, 1477-1484 (2012). [pdf] [arXiv] - Explicit Kummer surface formulas for arbitrary characteristic,
LMS J. Comput. Math. 13, 47-64 (2010). [pdf] [arXiv]
Note that the pdf files are preprint versions which may differ from the published versions.
PREPRINTS
- The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf (with Christian Curilla),
Preprint (2016), submitted. [arxiv] - Applying the Mordell-Weil sieve, Appendix to: Quadratic Chabauty and rational points I: p-adic heights by Jennifer Balakrishnan and Netan Dogra
Preprint (2016), submitted. [arxiv] - A geometric approach to constructing elements of K2 of curves (with Ulf Kühn),
Preprint (2015), submitted. [pdf] [arxiv]
TEACHING
- Sommersemester 2017
- Algebra II
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Wintersemester 2016/17
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Sommersemester 2016
- Algebra I
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Summer term 2015
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Winter term 2014/15
- Computational number theory
- Reading course Elliptic Curves II
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Summer term 2014
- Elliptic curves and cryptography
- Oberseminar Algebra/Geometry (with F. Heß, H.-G. Quebbemann and A. Stein)
- Teaching in Hamburg
- Diophantine Approximation, 2013
- Softwarepraktikum, 2011/12
- Prep course for math students, 2011/12
- Seminar on the arithmetic of elliptic curves, 2010/11
- Prep course for math students, 2010/11
CONFERENCES
- Together with Florian Heß and Andreas Stein organized the Workshop Arithmetic Geometry and Computer Algebra which took place from June 29, 2017 to July 1, 2017 in Oldenburg.
- Together with Jaap Top, Ben Moonen, Johannes Nicaise and Lenny Taelman I organized a NoGAGS-meeting, combined with the Belgian-Dutch Algebraic Geometry seminar. The meeting took place in Nijmegen in June 2015.
- Together with Yue Ren, I organized the Summer School in Algorithmic Mathematics 2013 which took place from September 2 to September 6 in Hamburg.
TALK SLIDES
- Computing integral points on hyperelliptic curves
Mathematics Colloquium, October 2014, Jacobs University Bremen - Rational points on Jacobians of hyperelliptic curves: Lecture I and Lecture II
Advanced Study Institute, August 2014, Ohrid - p-adic heights and integral points on hyperelliptic curves
Heights and Moduli spaces, June 2013, Lorentz Center, Leiden Universiteit - p-adic heights and integral points on hyperelliptic curves
Rational Points - Geometric, Analytic and Explicit Approaches, May 2013, Warwick - A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Forschungsseminar Arithmetische Geometrie, November 2012, Humboldt Universität zu Berlin - A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Arithmetic of L-functions, October 2012, University of Bristol - A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Rational points on curves: A p-adic and computational perspective, September 2012, Oxford - Computing canonical heights using arithmetic intersection theory
Séminaire de Cryptographie de Rennes, December 2011, Université Rennes I - Algorithmische Aspekte der Vermutung von Birch und Swinnerton-Dyer
Oberseminar Algebraische Geometrie, June 2011, LMU München - Arithmetik von Kummer Varietäten
Oberseminar Algebra, February 2011, Universität Oldenburg - Computing canonical heights on Jacobians
Rational points: Theory & Experiment, Workshop, May 2010, ETH Zürich - Explicit Kummer surface theory for arbitrary characteristic
Rational points on curves and higher-dimensional varieties, June 2009, University of Warwick
SHORT CV
since 01/14 | Juniorprofessor, University of Oldenburg | |||||||
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10/10-12/13 | Postdoc, University of Hamburg (my old Homepage) | |||||||
09/08-09/10 | PhD student, University of Bayreuth | |||||||
09/06-08/08 | PhD student, Jacobs University Bremen | |||||||
09/05-06/06 | Part III, University of Cambridge | |||||||
09/04-06/05 | Exchange year, Middle East Technical University Ankara | |||||||
10/02-07/05 | Undergraduate, TU Darmstadt |