**Office: **Blocker 641E

**E-mail: ptretkoff**-at-math.tamu.edu

- BSc Hons. Hons., Applied Mathematics (1978) and Pure Mathematics (1979), University of Sydney, Australia
- PhD, Mathematics, Nottingham University, United Kingdom, 1985
- Habilitation a diriger les recherches, Mathematics, University of Paris VI, Paris, France, 1995

- Number Theory
- Geometry, classical and non-commutative

Princeton University Press (Yellow Series) Book: Complex Ball Quotients and Line Arrangements in the Projective Plane Click here for more information

World Scientific Book: Periods and Special Functions in Transcendence Click here for more information

Files of selected publications (click here)

Some more papers:

Zariski-density of exceptional sets for hypergeometric functions

(appeared in Forum Mathematicum (20) 2 (2008), 187-199; joint with P-A Desrousseaux and M.D. Tretkoff)

Transcendence of values at algebraic points for certain higher order hypergeometric functions

(appeared in IMRN/15278 (61) 2005, 3835-3854; joint with P-A Desrousseaux and M.D. Tretkoff)

Transcendence of special values of Pochhamer functions

appeared in Int. J. of Number Theory (5) 4 (2009), 667-677; joint with M.D. Tretkoff

Transcendence of values of transcendental functions at algebraic points

Inaugural Monroe Martin lectures; to appear in JAMI Proceedings 2009, Johns Hopkins

appeared in Noncommutative Geometry, Arithmetic, and Related Topics,

Proceedings of the 21st JAMI Conference, Baltimore 2009, JHUP (2011), 279-295

A transcendence criterion for CM on some families of Calabi-Yau manifolds

with Marvin D. Tretkoff, in from Fourier Analysis and Number Theory to Radon

Transforms and Geometry - In memory of Leon Ehrenpreis, eds. H.M. Farkas,

R.C. Gunning, M.I. Knopp, B.A. Taylor, Developments in Math., Springer (2012).

Transcendence and CM on Borcea-Voisin towers of Calabi-Yau manifolds

Journal of Number Theory, Volume 152, July 2015, Pages 118-155.

K3 surfaces with algebraic period ratios have complex multiplication

International J. of Number Theory, Volume No. 11, Issue No. 5, (2015), Pages 1709-1724

Some papers in Noncommutative Geometry:

Automorphic Pseudodifferential Operators

(joint with Y. Manin and D. Zagier)

in Algebraic Aspects of Integrable Systems, Progr. Nonlinear Differential Equations Appl, 26, Birkhauser (1997), 17–47

The Gauss-Bonnet Theorem for the noncommutative two torus

(posted on the arxiv at http://arxiv.org/abs/0910.0188; joint with A. Connes)

(appeared in Noncommutative Geometry, Arithmetic, and Related Topics,

Proceedings of the 21st JAMI Conference, Baltimore 2009, JHUP (2011), 141-158)

Noncommutative Geometry and Number Theory

(Minicourse at Mount Holyoke Meeting on Noncommutative Geometry June 2000, in:

Surveys in Noncommutative Geometry, eds. N. Higson, J. Roe, CMI/AMS 2006, 143-189.)