Tim Dokchitser

Research

Most of my work concerns elliptic curves and the "standard conjectures" for L-functions associated to arithmetic varieties. For my algorithms to compute special values of these L-functions see ComputeL (Pari-based), Magma (starting from V2.12, July 2005, see L-functions and Artin Representations) and W. Stein's SAGE. I am an editor of the Glasgow Mathematical Journal and of the International Journal of Number Theory (IJNT).

(arxiv) Growth of Ш in towers for isogenous curves, with V. Dokchitser, January 2013
(arxiv) A remark on Tate's algorithm and Kodaira types, with V. Dokchitser, September 2012, to appear in Acta Arith.
(arxiv) Local invariants of isogenous elliptic curves, with V. Dokchitser, August 2012
(arxiv) Non-commutative Iwasawa theory for modular forms, with J. Coates, Z. Liang, W. Stein and R. Sujatha,
    March 2012, to appear in Proceedings of the LMS
(arxiv) Euler factors determine local Weil representations, with V. Dokchitser, December 2011
(arxiv) Brauer relations in finite groups II - quasi-elementary groups of order p^aq, with A. Bartel, October 2011
(arxiv) Surjectivity of mod 2ⁿ representations of elliptic curves, with V. Dokchitser, Math. Z., Volume 272, Issue 3-4 (2012), 961-964 (abs, pdf)
(arxiv) Brauer relations in finite groups, with A. Bartel, March 2011
(arxiv) Identifying Frobenius elements in Galois groups, with V. Dokchitser, to appear in Algebra and Number Theory (journal)
(arxiv) Notes on the parity conjecture, September 2010, to appear in the CRM Barcelona Advanced Courses in Mathematics
     "Elliptic Curves, Hilbert Modular Forms and Galois Deformations", Birkhauser, 2013 (publisher, amazon)
(arxiv) Solomon's induction in quasi-elementary groups, J. Group Theory 14 (2011), 49-51 (abs)
(arxiv) A note on the Mordell-Weil rank modulo n, with V. Dokchitser, J. Number Theory 131 (2011), 1833-1839 (abs)
(arxiv) Root numbers and parity of ranks of elliptic curves, with V. Dokchitser, Crelle, Volume 2011, Number 658, 39-64 (abs)
(arxiv) A note on Larsen's conjecture and ranks of elliptic curves, with V. Dokchitser, Bull. London Math. Soc. 41 no. 6 (2009), 1002-1008 (abs, pdf)
(arxiv) Elliptic curves with all quadratic twists of positive rank, with V. Dokchitser, Acta Arith. 137 (2009), 193-197 (abs)
(arxiv) Regulator constants and the parity conjecture, with V. Dokchitser, Invent. Math. 178, no. 1 (2009), 23-71 (abs, pdf)
     [Regulator constants - group-theoretic version]
(arxiv) Quotients of functors of Artin rings, Proc. Cam. Phil. Soc. 146 (2009), 531-534 (abs, pdf)
(arxiv) Self-duality of Selmer groups, with V. Dokchitser, Proc. Cam. Phil. Soc. 146 (2009), 257-267 (pdf)
(arxiv) On the Birch-Swinnerton-Dyer quotients modulo squares, with V. Dokchitser, Annals of Math. 172 no. 1 (2010), 567-596 (abs, pdf)
     [final version with a proof of the Parity Conjecture for Selmer ranks over Q]
(arxiv) Root numbers of elliptic curves in residue characteristic 2, with V. Dokchitser, Bull. London Math. Soc. 40 (2008), 516-524 (abs, pdf)
(arxiv) Parity of ranks for elliptic curves with a cyclic isogeny, with V. Dokchitser, J. Number Theory 128 (2008), 662-679 (pdf)
(arxiv) Ranks of elliptic curves in cubic extensions, Acta Arith. 126 (2007), 357-360 (abs)
(arxiv) Computations in non-commutative Iwasawa theory, with V. Dokchitser 
    and appendix by J. Coates and R. Sujatha, Proc. London Math. Soc. (3) 94 (2006), 211-272 (abs, pdf)
(arxiv) Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves, with R. de Jeu and D. Zagier
   Compositio Math. 142, Issue 02 (2006), 339-373 (pdf)
(arxiv) LLL & ABC, J. Number Theory 107, No.1 (2004), 161-167 (pdf)
    for additional algebraic ABC examples see ABC conjecture home page
(arxiv) Computing special values of motivic L-functions, Exper. Math. 13, No.2 (2004), 137-149 (pdf)

My Ph.D. thesis (2000, University of Utrecht, The Netherlands) is ``Deformations of p-divisible groups and p-descent on elliptic curves'' This is a link to the thesis, and on the right is a link to the genealogy tree  of my Ph.D. ancestors  (light) and some of  my Ph.D. relatives (dark).  Most of the data comes from the Mathematics Genealogy Project   at Minnesota State University.

Past events

LMS Regional meeting
"Arithmetic of L-functions", Bristol, 1-3 October, 2012

"Selmer Groups, Descent and Rank Distributions", Warwick, 24-28 September, 2012
workshop home page; part of the EPSRC Warwick Number Theory Symposium

School and Workshop on Computational Algebra and Number Theory, Trieste, June 18-29, 2012
school website

BSD Summer school, Sardinia, June 26-July 3, 2011
summer school website; notes from all 3 courses by Jim Brown.

BSD Conference, Cambridge, 4-6 May, 2011
program, participants, talk notes

SAGE Days 22: Computing with elliptic curves, MSRI Berkeley, June 2010
program and videos

Birch-Swinnerton-Dyer and Parity (Short course in CRM Barcelona, December 2009)
Course notes and references

Potential Modularity Day, 30 October 2009
program and videos