Prof. Dr. Jan Steffen Müller

• Explicit methods in number theory
• Arithmetic geometry

• 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.

• 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]

• 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

• 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.

• 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