Assistant Professor

Department of Mathematics

Bowdoin College

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

Office: 104 Searles Science Building

Office Hours (Fall 2015): by appointment (I am on teaching leave until the Spring 2016 semester)

Phone: 207-725-3574

Here is my CV if you are interested.

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:- A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors (with Michael Ben-Zvi and Alexander Ma, and an appendix by Alexandru Chirvasitu), submitted. (Also available at arXiv:1509.03618.)
- Infinite-dimensional diagonalization and semisimplicity (with Miodrag C. Ivanov and Zachary Mesyan), submitted. (Also available at arXiv:1502.05184.)
- A prime ideal principle for two-sided ideals, to appear in Communications in Algebra. (Also available at arXiv:1501.06808.)
- On discretization of C*-algebras (with Chris Heunen), submitted. (Also available at arXiv:1412.1721.)
- Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras (with Daniel Rogalski and James J. Zhang), to appear in Transactions of the AMS. (Also available at arXiv:1408.0536.)
- Quantum theory realizes
all joint measurability graphs (with Chris Heunen and Tobias Fritz),
Phys. Rev. A.
**89**(2014), no. 3, 032121. (Also available at arXiv:1310.3698.) - Skew Calabi-Yau algebras
and homological identities (with Daniel Rogalski and James J. Zhang),
Adv. Math.
**264**(2014), 308--354. (Also available at arXiv:1302.0437.) - Active lattices determine
AW*-algebras (with Chris Heunen),
J. Math. Anal. Appl.
**416**(2014), no. 1, 289--313. (Also available at arXiv:1212.5778.) - Sheaves that fail to represent
matrix rings, in
*Ring Theory and Its Applications*, Contemp. Math.**609**, 285--297, Amer. Math. Soc., Providence, RI, 2014. (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*, Contemp. Math.**480**, 263--288, 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:

- The spectrum problem for noncommutative rings and algebras, at the Oxford Advanced Seminar on Informatic Structures, May 22, 2015.
- 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.

Related to my research interests:

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: