Rahim Moosa's Homepage

Rahim N. Moosa

Associate Professor
Department of Pure Mathematics
University of Waterloo, MC 5049
Phone number : (519) 888-4567 ext. 32453
email: rmoosa at uwaterloo dot ca


I am on sabbatical this year, and a Research Member at MSRI until May 23rd.


Research interests:

Model theory (a branch of mathematical logic). Especially interactions with algebra, geometry and number theory.
Here is a link to the logic group homepage at Waterloo.

Preprints:

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

Model theory of fields with free operators in characteristic zero (with T. Scanlon). Revised August 2013. Submitted.

Some model theory of fibrations and algebraic reductions (with A. Pillay). To appear in Selecta.

Publications:

Countably categorical strongly minimal compact complex manifolds (with A. Pillay).
Proceedings of the American Mathematical Society, volume 140 (2012), number 5, 1785--1801.

Nonstandard methods for bounds in differential polynomial rings (with M. Harrison-Trainor and J. Klys).
Journal of Algebra, 360 (2012), 71--86

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.

Generalised Hasse-Schmidt varieties and their jet spaces (with T. Scanlon)
Proceedings of the London Mathematical Society, 2011, doi: 10.1112/plms/pdq055.

Jet and prolongation spaces (with T. Scanlon)
Journal de l'Institut de Mathematiques de Jussieu, volume 9 (2010), number 2, 391--430.

Model theory and complex geometry
Notices of the American Mathematical Society, volume 57 (2010), number 2, 230--235.

On canonical bases and internality criteria (with A. Pillay)
Illinois Journal of Mathematics, volume 52 (2008), number 3, 901--917.

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.

Differential arcs and regular types in differential fields (with A. Pillay and T. Scanlon)
J. Reine Angew. Math., volume 620 (2008), 35--54.

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.

Stable definablity and generic relations (with B. Kim)
Journal of Symbolic Logic, volume 72 (2007), number 4, 1163--1176.

Division points on subvarieties of isotrivial semiabelian varieties (with D. Ghioca)
International Mathematics Research Notices, volume 2006 (2006), Article ID 65437, 23 pages.

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.

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.

A nonstandard Riemann existence theorem
Transactions of the American Mathematical Society, volume 356 (2004), number 5, 1781--1797.

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.

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.


Unpublished notes:

Essential Saturation of LCK OT-manifolds (with Matei Toma). July 2013.

Compactness of cycle spaces and definability in o-minimal expansions of Ran (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.


Notes by students:

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

Geometric axioms for differentially closed fields with several commuting derivations. With Corrigendum.
By Omar Leon Sanchez. Journal of Algebra, 362 (2012), 107-116

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

A proof of omega-stability for m-DCF0. By Omar Leon Sanchez and Atul Sivaswamy. August 2009

Notes on "Groupoids, imaginaries and internal covers". By Oleg Chterental. April 2009


2013 Vita