Contact Details
Tel: 01865 279506.
Institute address:
Mathematical Institute
University of Oxford
2429 St Giles'
Oxford OX1 3LB
United Kingdom.

New College address:
New College
University of Oxford
Holywell Street
Oxford OX1 3BN
United Kingdom.

Academic links
My Genus 2 Site
Professor of Mathematics at the
Mathematical Institute,
University of Oxford,
since October 2006.
Fellow of New College,
University of Oxford,
since October 2005.
Oxford Number Theory Group.
Research Interests
My main area of research is
Number
Theory; more
specifically
(the arithmetic of)
Elliptic
Curves, Higher Genus Curves, and Arithmetic Algebraic
Geometry — especially Jacobians of curves, Chabauty techniques,
Visualisation of the ShafarevichTate Group,
and the BrauerManin Obstruction.
Publications/Preprints
Book
Articles
 E.V. Flynn.
Arbitrarily Large TateShafarevich Group on Abelian Surfaces
.
J. Number Theory 186 (2018), 248—258.
(pdf)
 E.V. Flynn.
Descent via (5,5)isogeny on Jacobians of genus 2 curves
.
J. Number Theory 153 (2015), 270—282.
(pdf)
 T. Chien, E.V. Flynn and S. Waldron.
Tight frames for cyclotomotic fields and other rational vector spaces
.
Linear Algebra and its Applications 476 (2015), 98—123.
(pdf)
 E.V. Flynn and D. Testa.
Finite Weil restriction of curves.
Monatsh. Math. 176 (2015), 197—218.
(pdf)
 D. Masser and U. Zannier, with an Appendix by E.V. Flynn.
Torsion points on families of abelian surfaces and Pell's
equation over polynomial rings.
J. Eur. Math. Soc. 17 (2015), 2379—2416.
(pdf)
 N. Bruin, E.V. Flynn and D. Testa.
Descent via (3,3)isogeny on Jacobians of genus 2 curves.
Acta Arith. 165 (2014), 201—223.
(pdf)
 E.V. Flynn, D. Testa and R. van Luijk.
Twocoverings of Jacobians of curves of genus two.
Proc. London Math. Soc. (3) 104 (2012), 387—429.
(pdf)
 E.V. Flynn.
Homogeneous Spaces and Degree 4 del Pezzo Surfaces.
Manuscripta Math. 129 (2009), 369—380.
(pdf)
 A. ArnthJensen and E.V. Flynn.
Nontrivial Sha in the Jacobian of an Infinite Family of Curves
of Genus 2.
J. Théor. Nombres Bordeaux 21 (2009), 1—13.
(pdf)
 E.V. Flynn and J. Wunderle.
Cycles of Covers.
Monatsh. Math. 157 (2009), 217—232.
(pdf)
 D. Harari and T. Szamuely, with an Appendix by E.V. Flynn.
Galois Sections for Abelianized Fundamental Groups.
Math. Ann. 157 (2009), 779—800.
(pdf)
 E.V. Flynn and C. Grattoni.
Descent Via Isogeny on Elliptic Curves with Large Rational
Torsion Subgroups.
J. Symb. Comput. 43 (2008), 293—303.
(pdf)
 M.J. Bright, N. Bruin, E.V. Flynn and A. Logan.
The BrauerManin Obstruction and Sha[2].
LMS J. Comput. Math. 10 (2007), 354—377.
(pdf)
 N. Bruin and E.V. Flynn.
Exhibiting Sha[2] on Hyperelliptic Jacobians.
J. Number Theory 118 (2006), 266—291.
(pdf)
 N. Bruin, E.V. Flynn, J. González and V. Rotger.
On Finiteness Conjectures for Modular Quaternion Algebras.
Math. Proc. Cam. Phil. Soc. 141 (2006), 383—408.
(pdf)
 N. Bruin and E.V. Flynn.
Towers of 2covers of Hyperelliptic Curves.
Trans. Amer. Math. Soc. 357 (2005), 4329—4347.
(pdf)
 E.V. Flynn.
The Hasse Principle and the BrauerManin Obstruction for Curves.
Manuscripta Math. 115 (2004), 437—466.
(pdf)
 N. Bruin and E.V. Flynn.
Rational Divisors in Rational Divisor Classes
in Algorithmic Number Theory,
Duncan Buell ed. Lecture Notes in Computer
Science, SpringerVerlag 3076 (2004), 132—139.
(pdf)
 E.V. Flynn and J. Redmond.
Application of Covering Techniques to Families of Curves.
J. Number Theory 101 (2003), 376—397.
(pdf)
 N. Bruin and E.V. Flynn.
NCovers of Hyperelliptic Curves.
Math. Proc. Camb. Phil. Soc. 134 (2003), 397—405.
(pdf)
 E.V. Flynn and J.L. Wetherell.
Covering Collections and a Challenge Problem of Serre.
Acta Arithmetica XCVIII.2 (2001), 197—205.
(pdf)
 E.V. Flynn, F. Leprévost, E.F. Schaefer,
W.A. Stein, M. Stoll and J.L. Wetherell.
Empirical Evidence for the Birch and SwinnertonDyer Conjectures
for Modular Jacobians of Genus 2 Curves.
Math. Comp. 70 (2001), 1675—1697.
(pdf)
 E.V. Flynn.
On QDerived Polynomials.
Proc. Edinburgh Math. Soc. 44 (2001), 103—110.
(pdf)
 E.V. Flynn.
Coverings of Curves of Genus 2.
Algorithmic Number Theory, Wieb Bosma ed.
Lecture Notes in Computer
Science 1838 (2000), SpringerVerlag, 65—84.
(pdf)
 E.V. Flynn and J.L. Wetherell.
Finding Rational Points on Bielliptic Genus 2 Curves.
Manuscripta Math., 100 (1999), 519—533.
(pdf)
 E.V. Flynn, B. Poonen and E. Schaefer.
Cycles of Quadratic Polynomials and Rational Points on
a Genus 2 Curve.
Duke Math. J. 90 (1997), 435—463.
(pdf)
 E.V. Flynn and N.P. Smart.
Canonical Heights on the
Jacobians of Curves of Genus 2 and the Infinite Descent.
Acta Arithmetica LXXIX.4 (1997), 333—352.
(pdf)
 E.V. Flynn.
A Flexible Method for Applying Chabauty's Theorem.
Compositio Math. 105 (1997), 79—94.
(pdf)
 E.V. Flynn.
The Arithmetic of Hyperelliptic Curves.
Algorithms in Algebraic Geometry, L. GonzálezVega, T. Recio eds.,
Progress in Mathematics 143 (1996), Birkhäuser
Boston, 165—175.
(pdf)
 E.V. Flynn.
On a Theorem of Coleman.
Manuscripta Math. 88 (1995), 447—456.
(pdf)
 E.V. Flynn.
Solving Diophantine Problems on Curves via Descent
on the Jacobian.
Number Theoretic and Algebraic Methods in Computer Science, Alf
van der Poorten, Igor Shparlinski and Horst G. Zimmer eds., World
Scientific (1995), 65—68.
(pdf)
 E.V. Flynn.
An Explicit Theory of Heights.
Trans. Amer. Math. Soc. 347, Number 8 (1995), 3003—3015.
(pdf)
 E.V. Flynn.
Descent via Isogeny in Dimension 2.
Acta Arithmetica LXVI.1 (1994), 23—43.
(pdf)
 E.V. Flynn.
The Group Law on the Jacobian of a Curve of Genus 2.
J. reine angew. Math. 439 (1993), 45—69.
(pdf)
 E.V. Flynn.
Sequences of Rational Torsions on Abelian Varieties.
Inventiones Math. 106 (1991), 433—442.
(pdf)
 E.V. Flynn.
Large Rational Torsion on Abelian Varieties.
J. Number Theory 36 (1990), 257—265.
(pdf)
 E.V. Flynn.
The Jacobian and Formal Group of a Curve of Genus 2
over an Arbitrary Ground Field.
Math. Proc. Camb. Phil. Soc. 107 (1990), 425—441.
(pdf)
Teaching
I am currently lecturing the Part C course
Elliptic Curves.
Previous Affiliations

Department of Mathematics,
University of Otago,
in Dunedin, New Zealand,
as an undergraduate, during 1980—1984.

Trinity College,
University of Cambridge,
as a PhD student, during 1985—1989.

Department of Mathematics,
University of Michigan,
as an Assistant Professor, during 1989—1990.

Robinson College,
University of Cambridge,
as a Research Fellow, during 1990—1994.
 Department of Pure Mathematics
and Mathematical Statistics,
University of Cambridge,
during 1985—1989 and 1990—1994.

Department of Mathematical Sciences,
University of Liverpool,
during 1994—2005 (Head of
Division
of Pure Mathematics: 2001—2005).
Visiting Positions:

Lorentz Center,
in Leiden, the Netherlands, during April 1999.

Department of Mathematics,
Santa Clara University,
California, as a Visiting Professor, during August 1999.

Department of Mathematics,
University of Southern California,
Los Angeles, as a Visiting Professor, during September 1999.

Department of Mathematics,
University of Colorado,
Boulder, Colorado, as a Visiting Professor, during October 1999.

Institut de Mathématiques,
Université Bordeaux,
as visiting Professeur Associé, June 2000.

Newton Institute,
during May—June 2002.

Department of Mathematics,
University of Sydney,
as a Visiting Professor, during January—April 2003.

Department of Mathematics,
Simon Fraser University,
Vancouver, as a Visiting Professor, during July—August 2004.

Mathematical Sciences Research Institute,
in Berkeley, California, during Oct—Dec 2000
and March—April 2006.

International Center for Transdisciplinary Studies,
Jacobs University,
Bremen, as an ICTS Fellow, during July—August 2007.

Department of Mathematics,
University of Auckland,
as a Visiting Professor, from September 2011 to February 2012.
Mathematical Links
Miscellaneous
This page last modified
by E.V. Flynn
Friday, 02Feb2018 03:08:20 GMT