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

Teaching

I will be teaching PMATH 733: Model theory and Set Theory in Winter 2015. Here is an Announcement and here are the Lecture Notes.

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

A note on subvarieties of powers of OT-manifolds (with M. Toma). Submitted 2014.

The model companion of differential fields with free operators (with O. Leon Sanchez). Submitted 2014.

Poisson algebras via model theory and differential-algebraic geometry (with J. Bell, S. Launois, and O. Leon Sanchez). Submitted 2014.

Differential-algebraic jet spaces preserve internality to the constants (with Z. Chatzidakis and M. Harrison-Trainor). Submitted 2013.



Publications

Geometric Stability Theory

Some model theory of fibrations and algebraic reductions (with A. Pillay).
Selecta Mathematica, volume 20 (2014), issue 4, 1067--1082.

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 compact complex manifolds

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.


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 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.



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-DCF0. By Omar Leon Sanchez and Atul Sivaswamy. 2009

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



2014 Vita