**Oxford Logic Seminar**

Thursdays during term; schedule.

**Future events**

**Introductory workshop:
Definability, Decidability, and Computability in Number Theory**

MSRI, August 24-28, 2020

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

MSRI, August-December 2020

** Past events**

Mathematical Institute, Oxford, September 5-7, 2019

Around Functional Transcendence

Mathematical Institute,
Oxford, June 26-29, 2018

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, DPhil (Oxford), 2018

Sebastian
Eterovic, DPhil (Oxford), 2019

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.