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:
Decidability in local and global fields
Proceedings of the International Congress of Mathematicians
volume 1
page 45-59
(31 May 2019)
Defining coarsenings of valuations
Proceedings of the Edinburgh Mathematical Society
issue 3
volume 60
page 665-687
(10 January 2017)
DEFINABLE HENSELIAN VALUATIONS
JOURNAL OF SYMBOLIC LOGIC
issue 1
volume 80
page 85-99
(March 2015)
Full text available
Uniformly defining p-henselian valuations
ANNALS OF PURE AND APPLIED LOGIC
issue 7-8
volume 166
page 741-754
(2015)
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 January 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