Rahim Moosa's Homepage
# Rahim N. Moosa

Professor

Department of Pure Mathematics

University of Waterloo, MC 5018

Phone number : (519) 888-4567 ext. 32453

email: rmoosa at uwaterloo dot ca

There will be a workshop on *Interactions between Model Theory and Arithmetic Dynamics* held at the **Fields Institute** July 25-29, 2016.

Here is a **poster**, and here is the **webpage**.

## Teaching

In Winter of 2016 I am teaching **Introduction to Commutative Algebra** (PMath 446/646).

## Research interests

Model theory (a branch of mathematical logic).
Especially interactions with algebra, geometry and number theory.

*Three recent applications of model theory* is a short exposition I wrote for MSRI's Spring 2014 newsletter, The Emissary.

Here is a link to the logic group homepage at Waterloo.

## Preprints

*
Finiteness theorems on hypersurfaces in partial differential-algebraic geometry*
(with J. Freitag). Submitted.

*
Model theory of compact complex manifolds with an automorphism*
(with M. Bays and M. Hils). To appear in the Transactions of the AMS.

*
The model companion of differential fields with free operators*
(with O. Leon Sanchez).
To appear in the Journal of Symbolic Logic.

*
Poisson algebras via model theory and differential-algebraic geometry*
(with J. Bell, S. Launois, and O. Leon Sanchez).

To appear in the Journal of the European Math Society.

*
Differential-algebraic jet spaces preserve internality to the constants*
(with Z. Chatzidakis and M. Harrison-Trainor).

To appear in the Journal of Symbolic Logic.

## Publications

### Model theory of compact complex manifolds

*
A note on subvarieties of powers of OT-manifolds*
(with M. Toma).

Bulletin Mathematiques de la Societe des Sciences Mathematiques de Roumanie, Tome 58 (2015), number 3, 311--316.

*
Countably categorical strongly minimal compact complex manifolds*
(with A. Pillay).

Proceedings of the American Mathematical Society, volume 140 (2012), number 5, 1785--1801.

*
Model theory and complex geometry*

Notices of the American Mathematical Society, volume 57 (2010), number 2, 230--235.

*
An essentially saturated surface not of Kaehler-type* (with R. Moraru and M. Toma)

Bull. Lond. Math. Soc., volume 40 (2008), number 5, 845--854.

*
Model theory and Kaehler geometry * (with A. Pillay)

In ** Model Theory with Applications to Algebra and Analysis Volume 1**
(Eds. Z. Chatzidakis, D. Macpherson, A. Pillay, A. Wilkie),

London Mathematical Society Lecture Note Series Nr 349, Cambridge University Press 2008, 167--195.

*
K-analytic versus CCM-analytic sets in nonstandard compact complex manifolds * (with S. Starchenko)

Fundamenta Mathematicae, volume 198 (2008), number 2, 139--148.

*
Strongly minimal groups in the theory of compact complex spaces * (with M. Aschenbrenner and T. Scanlon)

The Journal of Symbolic Logic, volume 71 (2006), number 2, 529--552.

*
On saturation and the model theory of compact Kaehler manifolds *

J. reine angew. Math., volume 586 (2005), 1--20.

*
The model theory of compact complex spaces*

** Logic Colloquium '01 **,
* Lecture Notes in Logic *, vol. 20 (M. Baaz, S. Friedman, and J. Krajicek, eds.),

Association for Symbolic Logic, 2005, pp. 317--349.

*
A nonstandard Riemann existence theorem *

Transactions of the American Mathematical Society, volume 356 (2004), number 5, 1781--1797.

### Geometric Stability Theory

*
Some model theory of fibrations and algebraic reductions*
(with A. Pillay).

Selecta Mathematica, volume 20 (2014), issue 4, 1067--1082.

**Correction** to the proof of Example 5.4.

*
A model-theoretic counterpart to Moishezon morphisms*

In ** Models, Logics, and Higher-Dimensional Categories: A tribute to the work of Mihaly Makkai**
(Eds. B. Hart, T. Kucera, A. Pillay, P. Scott, R. Seely),

Centre de Recherches Mathematiques Proceedings & Lecture Notes, Volume 53,
American Mathematical Society 2011, 177--188.

*
On canonical bases and internality criteria* (with A. Pillay)

Illinois Journal of Mathematics, volume 52 (2008), number 3, 901--917.

*
Stable definablity and generic relations * (with B. Kim)

Journal of Symbolic Logic, volume 72 (2007), number 4, 1163--1176.

### Model theory of fields

*
Model theory of fields with free operators in characteristic zero*
(with T. Scanlon).

Journal of Mathematical Logic.
2014, doi: 10.1142/s0219061314500093.

*
Nonstandard methods for bounds in differential polynomial rings *(with M. Harrison-Trainor and J. Klys).

Journal of Algebra, 360 (2012), 71--86

*
Generalised Hasse-Schmidt varieties and their jet spaces* (with T. Scanlon)

Proceedings of the London Mathematical Society, volume 103 (2011), number 2, 197--234.

*
Jet and prolongation spaces* (with T. Scanlon)

Journal de l'Institut de Mathematiques de Jussieu, volume 9 (2010), number 2, 391--430.

*
Differential arcs and regular types in differential fields* (with A. Pillay and T. Scanlon)

J. Reine Angew. Math., volume 620 (2008), 35--54.

*
On difference fields with quantifier elimination *

Bulletin of the London Mathematical Society, volume 33 (2001), number 6, 641--646.

*
A note on uniform definability and minimal fields of definition *

The Journal of Symbolic Logic, volume 65 (2000), number 2, 817--821.

### Model theory and diophantine geometry in positive characteristic

*
Division points on subvarieties of isotrivial semiabelian varieties * (with D. Ghioca)

International Mathematics Research Notices, volume 2006 (2006), Article ID 65437, 23 pages.

*
F-structures and integral points on semiabelian varieties over finite fields * (with T. Scanlon)

American Journal of Mathematics, volume 126 (2004), number 3, 473--522.

*
The Mordell-Lang conjecture in positive characteristic revisited * (with T. Scanlon)

**Model Theory and Applications**,

* Quaderni di matematica*, vol. 11 (L. Belair, Z. Chatzidakis, P. D'Aquino, D. Marker, M. Otero, F. Point, and A. Wilkie, eds.),

Seconda Universita di Napoli, 2002, p. 273--296.

## Unpublished notes

*Compactness of cycle spaces and definability in o-minimal expansions of ***R**_{an} (with Patrick Speissegger and Sergei
Starchenko).

(E-print at http://www.newton.cam.ac.uk/preprints/NI05040.pdf). July 2005.

*Jet spaces in complex analytic geometry: An Exposition.*

(E-print at http://arxiv.org/abs/math.LO/0405563). May 2004.

Ph.D. thesis:
Contributions to the model theory of fields and compact complex spaces.

University of Illinois at Urbana-Champaign, 2001.

## Students' work:

*
Contributions to the model theory of partial differential fields.
*Omar Leon Sanchez's PhD Thesis.
2013

*
Canonical bases in stable theories.
*
Ruizhang Jin's Master's Essay.
2013

*
A categorical generalization of Hrushovski's limit structure.
*
Chris Hawthorne's USRA report.
2013

*
An introduction to equations and equational theories.
*
Allen O'Hara's Master's Essay.
2011

*
The Mordell-Lang theorem from the Zilber dichotomy.
*
Chris Eagle's Master's Thesis.
2010

*
A proof of omega-stability for m-DCF*_{0}.
By Omar Leon Sanchez and Atul Sivaswamy.
2009

*
Notes on "Groupoids, imaginaries and internal covers".
*
Oleg Chterental's USRA report.
2009

2016
Vita