Prof. E. Victor Flynn

Contact Details

Tel: 01865 279506.

Institute address: Mathematical Institute University of Oxford 24-29 St Giles' Oxford OX1 3LB United Kingdom.

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

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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 Shafarevich-Tate Group, and the Brauer-Manin Obstruction.

Book

J.W.S. Cassels and E.V. Flynn. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2. London Mathematical Society Lecture Note Series 230. Cambridge University Press (1996). [231 pages]

Articles

• M. Corte-Real Santos and E.V. Flynn. Isogenies on Kummer Surfaces . To appear in Math. Comp. (2025). (pdf)
• E.V. Flynn and A. Shnidman. Arbitrarily large p-torsion in Tate-Shafarevich groups . To appear in J. Inst. Math. Jussieu (2025). (pdf)
• E.V. Flynn and K. Makdisi. An analog of the Edwards model for Jacobians of genus 2 curves . Res. Number Theory 10, 32 (2024). (pdf)
• N. Bruin, E.V. Flynn and A. Shnidman. Genus two curves with full level √3-structure and Tate-Shafarevich groups . Selecta Math. 29, 42 (2023). (pdf)
• E.V. Flynn. Arbitrarily large 2-torsion in Tate-Shafarevich groups of abelian varieties . Acta Arith. 191 (2019), 101—114. (pdf)
• E.V. Flynn and Y.B. Ti. Genus Two Isogeny Cryptography in Post-Quantum Cryptography, Springer (2019), 286—306. (pdf)
• E.V. Flynn. Arbitrarily Large Tate-Shafarevich 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. Two-coverings 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. Arnth-Jensen 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 Brauer-Manin 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 2-covers of Hyperelliptic Curves. Trans. Amer. Math. Soc. 357 (2005), 4329—4347. (pdf)
• E.V. Flynn. The Hasse Principle and the Brauer-Manin 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, Springer-Verlag 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. N-Covers 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 Swinnerton-Dyer Conjectures for Modular Jacobians of Genus 2 Curves. Math. Comp. 70 (2001), 1675—1697. (pdf)
• E.V. Flynn. On Q-Derived 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), Springer-Verlag, 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. González-Vega, 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)

I am currently lecturing the Part B course Algebraic Number Theory.

• Department of Mathematics, University of Otago, in Dunedin, New Zealand, as an undergraduate.
• Trinity College, University of Cambridge, as a PhD student.
• Department of Mathematics, University of Michigan, as an Assistant Professor.
• Robinson College, University of Cambridge, as a Research Fellow.
• Department of Pure Mathematics and Mathematical Statistics, University of Cambridge.
• Department of Mathematical Sciences, University of Liverpool (including four years as Head of Division of Pure Mathematics).

• Lorentz Center, in Leiden, the Netherlands.
• Department of Mathematics, Santa Clara University, California, as a Visiting Professor.
• Department of Mathematics, University of Southern California, Los Angeles, as a Visiting Professor.
• Department of Mathematics, University of Colorado, Boulder, Colorado, as a Visiting Professor.
• Institut de Mathématiques, Université Bordeaux, as visiting Professeur Associé.
• Newton Institute.
• Department of Mathematics, University of Sydney, as a Visiting Professor.
• Department of Mathematics, Simon Fraser University, Vancouver, as a Visiting Professor.
• Mathematical Sciences Research Institute, in Berkeley, California.
• International Center for Transdisciplinary Studies, Jacobs University, Bremen, as an ICTS Fellow.
• Department of Mathematics, University of Auckland, as a Visiting Professor.

• MAGMA

• My Dad's Webpage

This page last modified by E.V. Flynn
Tuesday, 24-Sep-2024 12:21:09 BST