Michael Stoll
Mathematisches Institut
Universität Bayreuth
95440 Bayreuth, Germany

Papers, Preprints and Lecture Notes

Arithmetic Geometry

[AG37]	How to solve a Diophantine equation (pdf, 208 kB) arXiv Extended notes of a talk given at the IMO 2009 (2010).
[AG36]	with S. Siksek: On a problem of Hajdu and Tengely (pdf, 195 kB) arXiv Preprint (2009), submitted for publication.
[AG35]	with P.G. Walsh and Pingzhi Yuan: On the Diophantine equation X² - (2^2m+1) Y⁴ = -2^2m Acta Arith. 139, 57-63 (2009).
[AG34]	Reduction theory of point clusters in projective space (pdf, 206 kB) arXiv Preprint (2009), submitted for publication.
[AG33]	with J.E. Cremona and T.A. Fisher: Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves (pdf, 446 kB) arXiv Preprint (2009), submitted for publication.
[AG32]	Rational Points on Curves of Genus 2: Experiments and Speculations (pdf, 135 kB) (Extended abstract of a talk in Dagstuhl, 2009), Dagstuhl Proceedings 09221
[AG31]	with N. Bruin: The Mordell-Weil sieve: Proving non-existence of rational points on curves (pdf, 447 kB) arXiv Preprint (2009), submitted for publication.
[AG30]	On the average number of rational points on curves of genus 2 (pdf, 629 kB) arXiv Preprint (2009).
[AG29]	Documentation for the ratpoints program (pdf, 188 kB) arXiv Manuscript (2009).
[AG28]	with N. Bruin: Two-cover descent on hyperelliptic curves (pdf, 310 kB) arXiv Math. Comp. 78, 2347-2370 (2009). DOI: 10.1090/S0025-5718-09-02255-8. Published online March 11, 2009.
[AG27]	Rational 6-cycles under iteration of quadratic polynomials (version 2008-06-11, pdf, 260 kB) arXiv London Math. Soc. J. Comput. Math. 11, 367-380 (2008). MAGMA script for the computations
[AG26]	Applications of the Mordell-Weil sieve (pdf, 113 kB) Oberwolfach Report 34/2007, Oberwolfach Reports 4, no. 3, 1967-1970 (2007).
[AG25]	with Y. Bugeaud, M. Mignotte, S. Siksek, and Sz. Tengely: Integral points on hyperelliptic curves (pdf, 300 kB) arXiv Algebra & Number Theory 2, No. 8, 859-885 (2008).
[AG24]	How to obtain global information from computations over finite fields (pdf, 23 kB) In: Higher-dimensional geometry over finite fields, NATO Science for Peace and Security Series: Information and Communication Security 16, (D. Kaledin, Y. Tschinkel, eds.), p. 189-196, IOS Press (2008).
[AG23]	with T.A. Fisher and E.F. Schaefer: The yoga of the Cassels-Tate pairing (new version 03/2009, pdf, 220 kB) arXiv Preprint (2007), submitted for publication.
[AG22]	with J.E. Cremona, T.A. Fisher, C. O'Neil and D. Simon: Explicit n-descent on elliptic curves. II. Geometry (Manuscript: pdf, 288 kB) arXiv J. reine angew. Math. 632, 63-84 (2009). DOI: 10.1515/CRELLE.2009.050. Published online June 16, 2009.
[AG21]	with N. Bruin: Deciding existence of rational points on curves: an experiment (pdf, 210 kB) arXiv Experiment. Math. 17, 181-189 (2008). See also my talk in Göttingen
[AG20]	with J.E. Cremona, T.A. Fisher, C. O'Neil and D. Simon: Explicit n-descent on elliptic curves. I. Algebra (Manuscript: pdf, 350 kB) arXiv J. reine angew. Math. 615, 121-155 (2008)
[AG19]	On the number of rational squares at fixed distance from a fifth power (Manuscript: pdf, 160 kB) arXiv Acta Arith. 125, 79-88 (2006)
[AG18]	Finite coverings and rational points (pdf, 94 kB) Oberwolfach Report 32/2005, Oberwolfach Reports 2, no. 3, 1824-1827 (2005).
[AG17]	with B. Poonen and E.F. Schaefer: Twists of X(7) and primitive solutions to x² + y³ = z⁷ (Manuscript: pdf, 560 kB) arXiv Duke Math. J. 137, 103-158 (2007)
[AG16]	Finite descent obstructions and rational points on curves (Manuscript: pdf, 399 kB) arXiv Algebra & Number Theory 1, 349-391 (2007). “Draft Version 8” (pdf, 520 kB) with some discussion of conjectures around “Effective Mordell”. See also my talk at MSRI, March 30, 2006. Note: the correct video may instead be here.
[AG15]	Independence of rational points on twists of a given curve (Manuscript: pdf, 240 kB) arXiv Compositio Math. 142, 1201-1214 (2006); DOI: 10.1112/S0010437X06002168, published online 25 Sep 2006
[AG14]	with T. Yang: On the L-function of the curves $y$ ² = x⁵ + A (Preprint version: dvi, 66 kB pdf, 250 kB) J. London Math. Soc. (2) 68, 273-287 (2003)
[AG13]	with J.E. Cremona: Minimal models for 2-coverings of elliptic curves (Preprint version: pdf, 211 kB) London Math. Soc. J. Comput. Math. 5, 220-243 (2002)
[AG12]	with J.E. Cremona: On the reduction theory of binary forms (Manuscript: pdf, 266 kB) J. reine angew. Math. 565, 79-99 (2003) See also my talk in Leiden, 2000 (dvi, 15 kB)
[AG11]	with E.F. Schaefer: How to do a p-descent on an elliptic curve Trans. Amer. Math. Soc. 356, 1209-1231 (2004) Long version: dvi (163 kB) pdf (360 kB)
[AG10]	On the height constant for curves of genus two, II Acta Arith. 104, 165-182 (2002) See also my talk in Leiden, 1999 (dvi, 24 kB)
[AG9]	with E.V. Flynn, F. Leprévost, E.F. Schaefer, W.A. Stein and J.L. Wetherell: Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves Math. Comp. 70, 1675-1697 (2001)
[AG8]	Implementing 2-descent for Jacobians of hyperelliptic curves Acta Arith. 98, 245-277 (2001)
[AG7]	On the arithmetic of the curves $y$ ² = x^l + A, II J. Number Theory 93, 183-206 (2002).
[AG6]	On the height constant for curves of genus two, Acta Arith. 90, 183-201 (1999).
[AG5]	with B. Poonen: A local-global principle for densities In: Scott D. Ahlgren (ed.) et al.: Topics in number theory. In honor of B. Gordon and S. Chowla. Kluwer Academic Publishers, Dordrecht. Math. Appl., Dordr. 467, 241-244 (1999).
[AG4]	with B. Poonen: The Cassels-Tate pairing on principally polarized abelian varieties arXiv Ann. of Math. (2) 150, 1109-1149 (1999).
[AG3]	On the arithmetic of the curves $y$ ² = x^l + A and their Jacobians J. reine angew. Math. 501, 171-189 (1998).
[AG2]	An example of a simple 2-dimensional abelian variety defined over Q with Mordell-Weil group of rank at least 20 C. R. Acad. Sci Paris 322. Série I, 849-851 (1996).
[AG1]	Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at least 19 C. R. Acad. Sci. Paris 321, Série I, 1341-1345 (1995).

Combinatorics

[CO2]	with D. Schleicher: An introduction to Conway's games and numbers (Manuscript: pdf, 300 kB) arXiv Moscow Mathematical Journal 6, 359-388 (2006).
[CO1]	Bounds for the length of recurrence relations for convolutions of P-recursive sequences Europ. J. Comb. 18, 707-712 (1997).

Mathematical Biology

[MB1]	with E. Geigant: Bifurcation analysis of an orientational aggregation model J. Math. Biol. 46, 537-563 (2003) (DOI 10.1007/s00285-002-0187-1)
[MB2]	with S. Schuster: A simple method to analyze resonators in fish hearing In: Elsner N., Wehner, R. (eds.): Proceedings of the 26th Göttingen Neurobiology Conference, Vol II, p. 303. Thieme, Stuttgart (1998).

Group Theory

[GR5]	Some group presentations with rational growth (dvi, 29 kB) Preprint (1995).
[GR4]	Asymptotics of the growth of 2-step nilpotent groups J. London Math. Soc. 58, 38-48 (1998).
[GR3]	Rational and transcendental growth series for the higher Heisenberg groups Invent. math. 126, 85-109 (1996).
[GR2]	Asymptotics of some number theoretic functions and an application to the growth of nilpotent groups (dvi, 370 kB) Bonner Mathematische Schriften 266 (1994) (doctoral thesis).
[GR1]	Regular geodesic languages for 2-step nilpotent groups In: A.J. Duncan, N.D. Gilbert, J. Howie (eds): Combinatorial and Geometric Group Theory, Edinburgh 1993, Cambridge University Press, Cambridge, LMS Lecture Note Series 204, 294-299 (1995).

Galois Theory

[GA2]	Construction of semiabelian Galois extensions Glasgow Math. J. 37, 99-104 (1995).
[GA1]	Galois groups over Q of some iterated polynomials Arch. Math. 59, 239-244 (1992).

Lecture Notes of Courses Taught at Jacobs University

[JN1]	Linear Algebra I (pdf, 530 kB) Notes from Fall 2006.
[JN2]	Linear Algebra II (pdf, 500 kB) Notes from Spring 2007.
[JN3]	Introductory Algebra (pdf, 530 kB) Notes from Fall 2005.
[JN4]	Introductory Number Theory (pdf, 530 kB) Notes from Spring 2006.
[JN5]	Introductory Complex Analysis (pdf, 765 kB) Notes from Spring 2007, with corrections.
[JN6]	Introductory Geometry: Second Half (Algebraic Geometry) (pdf, 255 kB) Notes from Fall 2005.
[JN7]	Integration and Manifolds (pdf, 549 kB) Notes from Fall 2007.

List of Jacobs University Courses

Other Course Notes

[CN1]	*Descent on Elliptic Curves* (pdf, 280 kB) arXiv Short Course taught at IHP in Paris, October 2004.
[CN2]	*Vector Bundles on Curves* (pdf, 590 kB) Notes of a course taught by G. Faltings at the MPI in Bonn, 1995.

Lecture Notes (in German) of Courses Taught in Düsseldorf

[LN1]	Abzählende Kombinatorik (pdf, 554 kB) Vorlesungsskript vom Wintersemester 1999/2000.
[LN2]	Elliptische Kurven I (pdf, 405 kB) Vorlesungsskript vom Sommersemester 2000.
[LN3]	Elliptische Kurven II (pdf, 495 kB) Vorlesungsskript vom Wintersemester 2000/2001.
[LN4]	Algebraische Kurven (pdf, 371 kB) Vorlesungsskript vom Wintersemester 2001/2002.

Talk Notes

	Diophantische Gleichungen und wie man manche von ihnen lösen kann (mathematischer Teil meiner Antrittsvorlesung am 29. Oktober 2009 in Bayreuth) pdf (130 kB)
	Rational Six-Cycles Under Quadratic Iteration (Slides of a talk at the GTEM 3rd annaul 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)
	Die Vermutung von Birch und Swinnerton-Dyer (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)
	Die Vermutung von Birch und Swinnerton-Dyer (Slides (in German) of a talk in Bremen, 2008-11-22) pdf (230 kB)
	Harmlose Gleichungen — Schwierige Lösung (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)
	Die Gleichung 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)
	Algorithmischer Beweis kombinatorischer Identitäten (German, Habilitationsvortrag, 1999-06-30) pdf (148 kB)

Michael Stoll, February 24, 2010