How to Solve Algebra Substitution Problems

Papers, preprints and lecture notes

An application of “Selmer group Chabauty” to arithmetic dynamics
(Slides of a talk at the MIT Number Theory Seminar, MIT, 2019-11-19) pdf (130 kB)
  Minimization and reduction of plane curves
(Slides of a talk at Rational Points on Irrational Varieties, IHP Paris, 2019-06-27) pdf (250 kB)
  Genus 2 curves with several points contained in an arithmetic progression
(Slides of a talk at Arithmetic Geometry, Number Theory, and Computation, MIT, 2018-08-24) pdf (340 kB)
  Simultaneous torsion in the Legendre family of elliptic curves
(Slides of a talk at Torsion groups and Galois representations of elliptic curves, University of Zagreb, 2018-06-29) pdf (1975 kB)
  Rational Diophantine quintuples and diagonal genus 5 curves
(Slides of a talk at Diophantine Problems, University of Manchester, 2017-09-15) pdf (155 kB)
  Rational points on curves in practice
(Slides of a talk at the Journées Algophantiennes Bordelaises, Université de Bordeaux, 2017-06-08) pdf (138 kB)
  Simultaneous torsion in the Legendre family of elliptic curves
(Slides of a talk at the workshop on Heights and applications to unlikely intersections, Fields Institute, Toronto, 2017-02-17) pdf (474 kB)
  The generalized Fermat equation x2 + y3 = z11
(Slides of a talk at the conference on Computational Aspects of Diophantine Equations, Salzburg, 2016-02-15) pdf (155 kB)
  Chabauty without the Mordell-Weil group
(Slides of a talk at Rational Points 2015, Schney, 2015-06-29) pdf (169 kB)
  Uniform bounds for the number of rational points on curves of low Mordell-Weil rank
(Slides of a talk at the conference on p-adic Methods in Number Theory, Berkeley, 2015-05-27) pdf (164 kB)
  Descent and covering collections
(Slides of a lecture series in Ohrid, 2014-09-01 / 03/05) Frey curves and the generalized Fermat equation
(Slides of a talk (in German) in Saarbrücken at the conferral of an honorary doctorate to Gerhard Frey, 2014-07-25) pdf (615 kB)
  Most odd degree hyperelliptic curves have only one rational point
(Slides of a talk in Bad Boll, 2014-03-04) pdf (183 kB)
  Many curves with few rational points
(Slides of a talk at the University of Warwick, 2012-09-25) pdf (127 kB)
  How to solve a Diophantine equation
(Lecture at the regional teacher training, 2012-06-27) pdf (170 kB)
  Explicit Kummer Varieties for Hyperelliptic Curves of Genus 3
(Slides of a talk in Luminy, 2012-01-17) pdf (93 kB)
  On a Problem of Hajdu and Tengely
(Slides of a contributed talk at ANTS-IX, 2010-07-23) pdf (126 kB)
  Torsion Points on Elliptic Curves over Quartic Number Fields
(Slides of the scientific part of my invited talk at ANTS-IX, 2010-07-22) pdf (128 kB)
  Diophantine equations and how to solve some of them
(mathematical part of my inaugural lecture on October 29, 2009 in Bayreuth) pdf (130 kB)
  Rational Six-Cycles Under Quadratic Iteration
(Slides of a talk at the GTEM 3rd annual meeting at Warwick, 2009-09-08) pdf (80 kB)
  Rational points on curves
(Slides of a talk at the Journées Arithmétiques, 2009-07-09) pdf (104 kB)
  Rational Points on Curves of Genus 2: Experiments and Speculations
(Slides of a talk in Dagstuhl, 2009-05-25) pdf (123 kB)
  The Birch and Swinnerton-Dyer conjecture
(Slides (in German) of a talk in Bayreuth, 2009-01-08) pdf (410 kB)
  Searching for Rational Points on Genus 2 Jacobians
(Slides of a talk in Banff, 2008-12-05) pdf (90 kB)
  The Birch and Swinnerton-Dyer conjecture
(Slides (in German) of a talk in Bremen, 2008-11-22) pdf (230 kB)
  Harmless equations - difficult solution
(Slides (in German) of a talk in Rostock, 2008-09-10) pdf (70 kB)
  Rational Points on Curves of Genus 2
(Slides of a colloquium talk at the University of Warwick, 2008-01-25) pdf (209 kB)
  How to Obtain Global Information From Computations Over Finite Fields
(Slides of a talk at a Summer School in Göttingen, 2007-07-05) pdf (90 kB)
  How to Determine the Set of Rational Points on a Curve
(Slides of a talk at the MEGA 2007 Conference in Strobl, 2007-06-28) pdf (143 kB)
  How to Find the Rational Points on a Rank 1 Genus 2 Curve
(Slides of a talk at a workshop in Leiden, 2007-05-14) pdf (170 kB)
  Coverings and Mordell-Weil Sieve
(Slides of a talk at a Banff workshop, 2007-02-06) pdf (91 kB)
  Deciding Existence of Rational Points on Genus 2 Curves: A Computational Experiment
(Slides of a talk at the Clay Summer School in Göttingen, 2006-07-21) pdf (95 kB)
  Finite Descent Obstructions and Rational Points
(Slides of a talk at MSRI, 2006-03-30) pdf (86 kB)
  Finite Coverings and Rational Points
(Notes of a talk in Oberwolfach, 2005-07-19) pdf (120 kB)
  x2 + y3 = z7
(Slides of a talk in Dagstuhl, 2004-05) pdf (118 kB)
  the equation x2 + y3 = z7
(Slides (in German) of a talk in Göttingen, 2004-01-15) pdf (89 kB)
  How many rational points can a curve have?
(Slides of a talk in Bordeaux, 2001-11-23) dvi (12 kB)
  Computation of canonical heights on genus 2 Jacobians
(Slides of a talk in Bordeaux, 2001-11-22) dvi (15 kB)
  Algorithmic proof of combinatorial identities
(German, habilitation lecture, 1999-06-30) pdf (148 kB)