Bristol
Mathematics
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Tim Dokchitser

Royal Society University Research Fellow
Heilbronn Chair in Arithmetic/Algebraic Geometry

Department of Mathematics
University Walk
Bristol
BS8 1TW

Office: 2.7 Howard House
tel 0117 954 56 23

  


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), William Stein's SAGE, and LMFDB/Artin representations. I am an editor of the Glasgow Mathematical Journal and of the International Journal of Number Theory (IJNT).

Recent publications/preprints:

(arxiv) Rational representations and permutation representations of finite groups, with A. Bartel, May 2014
(arxiv) A positive proportion of hyperelliptic curves have odd/even 2-Selmer rank, with V. Dokchitser,
    appendix to M. Bhargava, B. H. Gross, X. Wang "Pencils of quadrics and the arithmetic of hyperelliptic curves", October 2013
(arxiv) Euler factors determine local Weil representations, with V. Dokchitser, to appear in Crelle (abs)
(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, Acta Arith. 160 (2013), 95-100 (abs)
(arxiv) Local invariants of isogenous elliptic curves, with V. Dokchitser, August 2012, to appear in Trans. Amer. Math. Soc. (journal)
(arxiv) Non-commutative Iwasawa theory for modular forms, with J. Coates, Z. Liang, W. Stein and R. Sujatha,
    Proc. London Math. Soc. 107(3), 2013, 481-516 (abs, pdf)
(arxiv) Brauer relations in finite groups II - quasi-elementary groups of order paq, with A. Bartel, to appear in J. Group Theory (abs)
(arxiv) Surjectivity of mod 2n representations of elliptic curves, with V. Dokchitser, Math. Z., Vol. 272, Issue 3-4 (2012), 961-964 (abs, pdf)
(arxiv) Brauer relations in finite groups, with A. Bartel, March 2011, to appear in J. Eur. Math. Soc.
(arxiv) Identifying Frobenius elements in Galois groups, with V. Dokchitser, Algebra and Number Theory 7 (2013), no. 6, 1325-1352 (abs)
(arxiv) Notes on the parity conjecture, September 2010, 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 (Apr 2007) 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.

  PhD genealogy tree

Future/past events

British Mathematical Colloquium
Bristol, March 21-24, 2016

Elliptic curves, modular forms and Iwasawa theory
Conference in honour of the 70th birthday of John Coates, Cambridge, March 25-27, 2015

2nd EU/US Summer School and Workshop on Automorphic Forms and Related Topics
Bristol, June 30-July 14, 2014 - L-functions course lecture notes (3 lectures)

Average ranks of elliptic curves (after Bhargava and Shankar)
Short lecture course in Poznan, May 2014, lecture notes by Zędrzej Garnek

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


Alex Bartel Julio Brau Vladimir Dokchitser Adam Morgan Rachel Newton