Algebra 2  TCC Galois representations 
Bristol Mathematics 
Seminars He, Li, Ag 
ComputeL  Hyperelliptic curve database 
Tim DokchitserHeilbronn Chair in Arithmetic/Algebraic Geometry
Department of Mathematics
Office: 2.7 Howard House 

Most of my work concerns elliptic curves, the BirchSwinnertonDyer conjecture, Galois representations and Lfunctions. All of my algorithms are in Magma: Lfunctions, Artin Representations, and Galois Representations (new); the original Paribased package ComputeL to compute special values of Lfunctions is also available through William Stein's SAGE, and a database of Artin representations is included in 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)
Quotients of hyperelliptic curves and etale cohomology,
with V. Dokchitser, November 2015
(arxiv)
Rational representations and permutation representations of finite groups,
with A. Bartel, Math. Ann. 364, Issue 1 (2016), 539558
(abs)
(arxiv)
A positive proportion of hyperelliptic curves have odd/even 2Selmer rank,
with V. Dokchitser, October 2013, appendix to
M. Bhargava, B. H. Gross, X. Wang "Pencils of quadrics and the arithmetic of
hyperelliptic curves", to appear in J. Amer. Math. Soc.
(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, Compositio Math. 151 (2015), 19812005
(abs)
(arxiv)
Local invariants of isogenous elliptic curves, with V. Dokchitser,
Trans. Amer. Math. Soc. 367 (2015), 43394358
(abs,
pdf)
(arxiv)
A remark on Tate's algorithm and Kodaira types, with V. Dokchitser, Acta
Arith. 160 (2013), 95100 (abs,
pdf)
(arxiv)
Noncommutative Iwasawa theory for modular forms,
with J. Coates, Z. Liang, W. Stein and R. Sujatha,
Proc. London Math. Soc. 107(3), 2013, 481516
(abs,
pdf)
(arxiv) Brauer relations in
finite groups II  quasielementary groups of order p^{a}q, with
A. Bartel, J. Group Theory 17, Issue 3 (2014), 381393.
(abs)
(arxiv)
Surjectivity of mod 2^{n} representations of elliptic curves, with V. Dokchitser,
Math. Z., Vol. 272, Issue 34 (2012), 961964
(abs,
pdf)
(arxiv) Brauer relations in finite groups, with A. Bartel, J. Eur. Math. Soc. 17 (2015), 24732512
(arxiv) Identifying Frobenius
elements in Galois groups, with V. Dokchitser, Algebra and Number Theory 7 (2013), no. 6, 13251352
(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 quasielementary groups, J. Group Theory 14 (2011), 4951
(abs)
(arxiv)
A note on the MordellWeil rank modulo n, with V. Dokchitser, J. Number Theory 131 (2011), 18331839
(abs)
(arxiv) Root numbers and parity
of ranks of elliptic curves, with V. Dokchitser,
Crelle, Volume 2011, Number 658, 3964
(abs)
(arxiv) A note on Larsen's conjecture and ranks of elliptic curves,
with V. Dokchitser, Bull. London Math. Soc. 41 no. 6 (2009), 10021008
(abs,
pdf)
(arxiv) Elliptic curves with all quadratic twists of positive rank, with V. Dokchitser, Acta Arith. 137 (2009), 193197
(abs)
(arxiv) Regulator constants and the parity conjecture, with V. Dokchitser, Invent. Math. 178, no. 1 (2009), 2371
(abs, pdf)
[Regulator constants  grouptheoretic version]
(arxiv) Quotients of functors of Artin rings,
Proc. Cam. Phil. Soc. 146 (2009), 531534
(abs,
pdf)
(arxiv) Selfduality of Selmer groups, with V. Dokchitser,
Proc. Cam. Phil. Soc. 146 (2009), 257267 (pdf)
(arxiv) On the BirchSwinnertonDyer quotients modulo squares,
with V. Dokchitser, Annals of Math. 172 no. 1 (2010), 567596
(abs,
pdf)
[final version (Apr 2007) with the 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), 516524
(abs, pdf)
(arxiv) Parity of ranks for elliptic curves with a cyclic isogeny, with V. Dokchitser, J. Number Theory 128 (2008), 662679
(pdf)
(arxiv) Ranks of elliptic curves in cubic extensions,
Acta Arith. 126 (2007), 357360 (abs)
(arxiv) Computations in noncommutative Iwasawa theory, with V. Dokchitser
and appendix by J. Coates and R. Sujatha, Proc. London Math. Soc. (3) 94 (2006), 211272
(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), 339373
(pdf)
(arxiv) LLL & ABC, J. Number Theory 107, No.1 (2004), 161167
(pdf)
for additional algebraic ABC examples see
ABC conjecture home page
(arxiv)
Computing special values of motivic Lfunctions, Exper. Math. 13, No.2 (2004), 137149
(pdf)
My Ph.D. thesis (2000,
University of Utrecht, The Netherlands) is
``Deformations of pdivisible groups and pdescent on elliptic curves'' This is a link to the
thesis, and on the right is
a link to the genealogy tree 

Curves and Lfunctions
Summer school and workshop, ICTP Trieste, August 28  September 8, 2017
British Mathematical Colloquium
Bristol, March 2124, 2016
LMSCMI Summer school on Diophantine Equations
Baskerville Hall, September 1420, 2015
Elliptic curves, modular forms and Iwasawa theory
Conference in honour of the 70th birthday of John Coates, Cambridge, March 2527, 2015
Algebraic Geometry
TCC graduate lecture course, with lecture notes, Spring 2015.
2nd EU/US Summer School and Workshop on Automorphic Forms and Related Topics
Bristol, June 30July 14, 2014 
Lfunctions 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
Lfunctions", Bristol, 13 October, 2012
"Selmer Groups, Descent and Rank Distributions",
Warwick, 2428 September, 2012
workshop home page; part of the
EPSRC Warwick Number Theory Symposium
School and Workshop on Computational Algebra and Number Theory, Trieste, June 1829, 2012
school website
BSD Summer school, Sardinia, June 26July 3, 2011
notes from all 3 courses by
Jim Brown.
BSD Conference, Cambridge, 46 May, 2011
program, participants, talk notes
SAGE Days 22: Computing with elliptic curves, MSRI Berkeley, June 2010
program and videos
BirchSwinnertonDyer 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  Christopher Doris  Adam Morgan  Rachel Newton 