Assistant Professor

Department of Mathematics

Bowdoin College

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

Office: 104 Searles Science Building

Office Hours (Spring 2016): Monday 11am-12pm, Tuesday 3-4pm, Wednesday 2-3pm.

Phone: 207-725-3574

Here is my CV if you are interested.

- Math 1750, Integral Calculus (Advanced Section)
- Math 3702, Advanced Topics in Rings and Number Theory

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

My research focuses on Ring Theory (both noncommutative and commutative rings) and Noncommutative Geometry (including noncommutative algebraic geometry). I am often 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), to appear in Israel Journal of Mathematics. (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: