Status:
University Lecturer at the Mathematical Institute (Logic Group) and Tutorial Fellow at LMH
+44 1865 273568
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
Defining Z in Q
ANNALS OF MATHEMATICS
issue 1
volume 183
page 73-93
(January 2016)
Full text available
On the 'Section Conjecture' in anabelian geometry
Journal fur die reine und angewandte Mathematik (Crelles Journal)
issue 588
volume 2005
page 221-235
(November 2005)
Solvable absolute Galois groups are metabelian
Inventiones mathematicae
issue 1
volume 144
page 1-22
(April 2001)
FROM P-RIGID ELEMENTS TO VALUATIONS (WITH A GALOIS-CHARACTERIZATION OF P-ADIC FIELDS)
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
volume 465
page 165-182
(1995)
Full text available
Undecidability in number theory
MODEL THEORY IN ALGEBRA, ANALYSIS AND ARITHMETIC
volume 2111
page 159-195
(2014)
Full text available
Recent Publications:
DEFINING COARSENINGS OF VALUATIONS
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
issue 3
volume 60
page 665-687
(August 2017)
Full text available
Uniformly defining p-henselian valuations
Annals of Pure and Applied Logic
issue 7-8
volume 166
page 741-754
(1 January 2015)
Uniformly defining p-henselian valuations
ANNALS OF PURE AND APPLIED LOGIC
issue 7-8
volume 166
page 741-754
(2015)
Full text available
Definable henselian valuations
submitted to Journal of Symbolic Logic on 28 Oct 2012
(29 October 2012)
Full text available
Schlanke Körper (Slim fields).
J. Symb. Log.
issue 2
volume 75
page 481-500
(2010)
Projective extensions of fields
Journal of the London Mathematical Society
issue 3
volume 73
page 639-656
(June 2006)
Products of absolute galois groups
International Mathematics Research Notices
issue 24
page 1465-1486
(18 May 2005)
The regular inverse Galois problem over non-large fields
Journal of the European Mathematical Society
issue 4
volume 6
page 425-434
(1 January 2004)
Defining transcendentals in function fields
The Journal of Symbolic Logic
issue 3
volume 67
page 947-956
(September 2002)
Abelian subgroups of pro-p galois groups
Transactions of the American Mathematical Society
issue 6
volume 350
page 2473-2485
(1 December 1998)
Research interests:
Model theory and arithmetic of fields, valuation theory, Galois theory, Hilbert's 10th problem, anabelian Geometry, number theory
Prizes, awards, and scholarships:
Studienstiftung des deutschen Volkes, Dornier-Forschungspreis, Heisenberg-Fellow (DFG), Invited Speaker at ICM Rio 2018