# 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)

**Minimization and reduction of plane curves**(Slides of a talk at

**Rational Points on Irrational Varieties**, IHP Paris, 2019-06-27)

**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)

**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)

**Rational Diophantine quintuples and diagonal genus 5 curves**(Slides of a talk at

**Diophantine Problems**, University of Manchester, 2017-09-15)

**Rational points on curves in practice**(Slides of a talk at the

**Journées Algophantiennes Bordelaises**, Université de Bordeaux, 2017-06-08)

**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)

**The generalized Fermat equation***x*^{2}+*y*^{3}=*z*^{11}(Slides of a talk at the conference on

**Computational Aspects of Diophantine Equations**, Salzburg, 2016-02-15)

**Chabauty without the Mordell-Weil group**(Slides of a talk at

**Rational Points 2015**, Schney, 2015-06-29)

**Uniform bounds for the number of rational points on curves of low Mordell-Weil rank**(Slides of a talk at the conference on

**, Berkeley, 2015-05-27)**

*p*-adic Methods in Number Theory

**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)

**Most odd degree hyperelliptic curves have only one rational point**(Slides of a talk in Bad Boll, 2014-03-04)

**Many curves with few rational points**(Slides of a talk at the University of Warwick, 2012-09-25)

**How to solve a Diophantine equation**(Lecture at the regional teacher training, 2012-06-27)

**Explicit Kummer Varieties for Hyperelliptic Curves of Genus 3**(Slides of a talk in Luminy, 2012-01-17)

**On a Problem of Hajdu and Tengely**(Slides of a contributed talk at ANTS-IX, 2010-07-23)

**Torsion Points on Elliptic Curves over Quartic Number Fields**(Slides of the scientific part of my invited talk at ANTS-IX, 2010-07-22)

**Diophantine equations and how to solve some of them**(mathematical part of my inaugural lecture on October 29, 2009 in Bayreuth)

**Rational Six-Cycles Under Quadratic Iteration**(Slides of a talk at the GTEM 3rd annual meeting at Warwick, 2009-09-08)

**Rational points on curves**(Slides of a talk at the Journées Arithmétiques, 2009-07-09)

**Rational Points on Curves of Genus 2: Experiments and Speculations**(Slides of a talk in Dagstuhl, 2009-05-25)

**The Birch and Swinnerton-Dyer conjecture**(Slides (in German) of a talk in Bayreuth, 2009-01-08)

**Searching for Rational Points on Genus 2 Jacobians**(Slides of a talk in Banff, 2008-12-05)

**The Birch and Swinnerton-Dyer conjecture**(Slides (in German) of a talk in Bremen, 2008-11-22)

**Harmless equations - difficult solution**(Slides (in German) of a talk in Rostock, 2008-09-10)

**Rational Points on Curves of Genus 2**(Slides of a colloquium talk at the University of Warwick, 2008-01-25)

**How to Obtain Global Information From Computations Over Finite Fields**(Slides of a talk at a Summer School in Göttingen, 2007-07-05)

**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)

**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)

**Coverings and Mordell-Weil Sieve**(Slides of a talk at a Banff workshop, 2007-02-06)

**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)

**Finite Descent Obstructions and Rational Points**(Slides of a talk at MSRI, 2006-03-30)

**Finite Coverings and Rational Points**(Notes of a talk in Oberwolfach, 2005-07-19)

*x*^{2}+*y*^{3}=*z*^{7}(Slides of a talk in Dagstuhl, 2004-05)

**the equation***x*^{2}+*y*^{3}=*z*^{7}(Slides (in German) of a talk in Göttingen, 2004-01-15)

**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)

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