**Oxford Logic
Seminar**

Tuesdays
during term; schedule.**Future
events**

**Definability, Decidability, and Computability in Number Theory**

MSRI, August-December 2020

**Around Functional Transcendence**

Mathematical Institute, Oxford, June 26-29, 2018

Past events

Workshop on O-minimality and Diophantine Applications

Fields Institute, June 19-23, 2017

Thematic
Programme on Unlikely Intersections, Heights, and Efficient
Congruencing

Fields
Institute, Toronto, January-June 2017

Oberwolfach, 30 April - 6 May, 2017

Konstanz, July 18-23, 2016

Geometry, Number Theory, and Logic

Oxford, July 6, 2016

Oxford, July 5-6, 2016

Future
Directions in Model Theory and Analytic Functions

MIMS,
Manchester, 7-10 July, 2015

Functional
Transcendence around Ax-Schanuel

CMI
workshop, Oxford, 29 September - 3 October, 2014

Model
Theory in Geometry and Arithmetic

MSRI, 12-16 May,
2014*L*-functions,
Spectra and Equidistribution

IAS,
Hebrew University of Jerusalem, 11-19 December, 2013

Synergies
And Vistas in Analytic Number Theory

Oxford, 3-7 September,
2012

Miniworkshop
in O-minimality and Diophantine Geometry

Oxford,
24-25 August, 2012

Unlikely
intersections in algebraic groups and Shimura varieties

AIM
workshop held at Centro De Giorgi, Scuola Normale Pisa, March 28
-April 1, 2011

Workshop
in Computational Number Theory

July 7-9, 2005, University of
Cantabria, Santander, Spain, part of FoCM'05

Far
Hills Workshop on L-functions and p-adic cohomology: computational
perspectives

CICMA-CRM workshop, 2-4 January 2004.

Future
directions in algorithmic number theory

AIM workshop, Palo
Alto, March 24-28, 2003**Lecture
notes and surveys**

Clay
Research Conference 2011

``Diophantine geometry via model
theory'', video here.

LMS-EPSRC
Shortcourse on O-minimality and Diophantine Geometry

Manchester,
July 8-12, 2013

Functional transcendence via o-minimality (5
lectures), pdf notes here.

The
copyright in these lecture notes belongs to CUP. They will appear in
final form

in a volume published by CUP. These notes may only be
used for non-commercial purposes.

ICM, Seoul
2014

``O-minimality and Diophantine geometry'',

Expanded
version of talk as preprint here,
slides here, and the talk itself can be
viewed here.

Clay
Research Conference 2014

``The Schanuel paradigm'', slides here,
video on Clay Mathematics Institute website here.**Graduate
students**

My
thesis was supervised by Peter Sarnak, so I belong to a large
``academic family''; see here.

My
students:

Andrew
Potter, PhD (Bristol), 2010

Lee Butler, PhD (Bristol), 2011

Adam Harris, DPhil (Oxford), 2013, joint supervision with Boris Zilber

Vahagn Aslanyan, DPhil (Oxford), 2017, joint supervision with Boris Zilber

Haden Spence, current

Sebastian Eterovic, current

John Armitage, current

Guy Fowler, current

**Some
more papers** (preprints
may differ from final published form)

Frobenius
maps of abelian varieties and finding roots of unity in finite
fields,

Math.
Comp.**55**
(1990), 745--763, preprint.

Geometric
postulation of a smooth function and the number of rational points,

Duke Math. J.**63**
(1991), 449--463, preprint
version by permission of the publisher.

Geometric and
arithmetic postulation of the exponential function,*J.
Austral. Math. Soc. Ser. A*
**54**
(1993), 111--127, preprint.

Density
of integer points on plane algebraic curves,

IMRN**1996**
(1996), 903--912, preprint.

(with
F. R. Villegas) Concordant sequences and integral-values entire
functions,

Acta
Arith.**88**
(1999), 239--268, preprint.

(with
H. W. Lenstra and C. Pomerance) A hyperelliptic smoothness tes, II,

Proc. London
Math. Soc. (3)**84**
(2002), 105--146, preprint.

Entire
functions having a concordant value sequence,

Israel
J. Math.**134**
(2003), 317--343, preprint.

Integer
points on the dilation of a subanalytic set,

Quarterly
J. Math.**55**
(2004), 207--223, preprint.

Note
on Carlson's Theorem,

Rocky
Mountain Math. J.**35**
(2005), 2107--2111, preprint.

Rational
points on a subanalytic surface, *Ann.
Inst. Fourier* **55**
(2005), 1501--1516, preprint.

The
density of rational points on a Pfaff curve, *Ann.
Fac. Sci. Toulouse Math. (6)*
**16**
(2007), 635--645, preprint.

Entire
functions sharing arguments of integrality, II,

Publ.
Math. Debrecen**73**
(2008), 215--231, preprint.

Entire
functions sharing arguments of integrality, I,

Int.
J. Number Theory**5**
(2009), 339--353, preprint.

On
the algebraic points of a definable set, *Selecta
Math. (N.S.)* **15**
(2009), 151--170, preprint.

The final published version is available at link.springer.com,
here.

Rational
points of definable sets and results of Andre-Oort--Manin-Mumford
type,*IMRN, *2009,
2476--2507, available here.

Counting
rational points on a certain exponential-algebraic surface,*Ann.
Inst. Fourier* **60**
(2010), 489--514, preprint. And correction (all theorems remain true).

Modular
Ax-Lindemann-Weierstrass with derivatives*Notre
Dame J. Formal Logic*
**54**
(2013), 553--565 (Oleron volume in honour of Pillay).

Preprint
version here.

Special point
problems with elliptic modular surfaces,*Mathematika*
**60**
(2014), 1-31, doi:10.1112/S0025579313000168, copyright UCL.

Preprint
version here.

Compositio 148 (2012), 1-27. Preprint version here.

(with J. Tsimerman) The Andre-Oort conjecture for the moduli space of Abelian surfaces,

Compositio 149 (2013), 204-216, arXiv version here.

(with L. Capuano, D. Masser, and U. Zannier)

Rational points on Grassmannians and unlikely intersections in tori,

Bull. LMS 48 (2016), 141-154. Published version here.

(with J. Tsimerman)

Multiplicative relations among singular moduli,

arXiv preprint here, Annali della Scuola Normale Superiore di Pisa, to appear.

On a modular Fermat equation, arXiv preprint here,

Commentarii Mathematici Helvetici 92 (2017), 85-103.