Assistant Professor

Department of Mathematics

Bowdoin College

Email: reyes@bowdoin (where "bowdoin" means "bowdoin dot edu").

Office: 104 Searles Science Building.

Spring 2014 Office Hours: Tues 3-4pm, Wed 3-4pm, Thurs 12-1pm.

Phone: 207-725-3574.

You can see my CV if you are interested.

- Math 1700, Integral Calculus
- Math 3602, Advanced Topics in Algebra

Students can access online course materials by logging in to Blackboard.

My research interests lie in Ring Theory (both noncommutative and commutative rings) and Noncommutative Geometry (including noncommutative algebraic geometry). I am also interested in cases where these ideas intersect with the study of category theory, operator algebras, and quantum physics.

Here are some preprints of my papers:- Quantum theory realizes all joint measurability graphs (with Chris Heunen and Tobias Fritz), to appear in Phys. Rev. A. (Also available at arXiv:1310.3698.)
- Skew Calabi-Yau algebras and homological identities (with Daniel Rogalski and James J. Zhang), submitted. (Also available at arXiv:1302.0437.)
- Active lattices determine AW*-algebras (with Chris Heunen), to appear in J. Math. Anal. Appl. (Also available at arXiv:1212.5778.)
- Sheaves that fail to represent matrix rings, to appear in the proceedings of the 31st Dennison Mathematics Conference in honor of T.Y. Lam. (Also available at arXiv:1211.4005.)
- Diagonalizing matrices over AW*-algebras
(with Chris Heunen), J. Funct. Anal.
**264**(2013), no. 8, 1873--1898. (Also available at arXiv:1208.5120.) - Obstructing extensions of the functor Spec to
noncommutative rings, Israel J. Math.
**192**(2012), no. 2, 667--698. (Also available at arXiv:1101.2239.) - Noncommutative
generalizations of theorems of Cohen and Kaplansky, Algebr. Represent. Theory
**15**(2012), no. 5, 933--975. (Also available at arXiv:1007.3701.) - A
one-sided Prime Ideal Principle for noncommutative rings, Journal of Algebra and Its
Applications
**9**(2010), no. 6, 877--919. (Also available at arXiv:0903.5295.) - Oka and
Ako Ideal Families in Commutative Rings (with T.Y. Lam),
*Rings, Modules, and Representations*, 263--288, Contemp. Math., 480, Amer. Math. Soc., Providence, RI, 2009. - A Prime Ideal
Principle in commutative algebra (with T.Y. Lam), Journal of Algebra
**319**(2008), no. 7., 3006--3027.

Here are some slides from selected talks that I have given:

- Skew Calabi-Yau algebras and homological identities, at the Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society, June 30, 2013.

Some websites where I like to answer, ask, and read mathematics questions:

Here are some links to Wikipedia pages that concern various aspects of my work: