Assistant Professor

Department of Mathematics

Bowdoin College

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

Office: 104 Searles Science Building

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

Phone: 207-725-3574

Here is my CV, which is updated irregularly.

- Math 1750A, Integral Calculus (Advanced Section)
- Math 2000A, Linear Algebra

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.

Below is the list of my publications and preprints:-
*Discretization of C*-algebras*(with Chris Heunen), to appear in Journal of Operator Theory. (This paper supersedes arXiv:1412.1721.)

[ PDF ] [ arXiv ] -
*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.

[ PDF ] [ arXiv ] *Infinite-dimensional diagonalization and semisimplicity*(with Miodrag C. Ivanov and Zachary Mesyan), to appear in Israel Journal of Mathematics.

[ PDF ] [ arXiv ]*A prime ideal principle for two-sided ideals*, Comm. Alg.**44**(2016), no. 11, 4585-4608.

[ PDF ] [ arXiv ] [ journal ]*Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras*(with Daniel Rogalski and James J. Zhang), to appear in Transactions of the AMS.

[ PDF ] [ arXiv ] [ journal ]-
*Quantum theory realizes all joint measurability graphs*(with Chris Heunen and Tobias Fritz), Phys. Rev. A.**89**(2014), no. 3, 032121.

[ PDF ] [ arXiv ] [ journal ] -
*Skew Calabi-Yau algebras and homological identities*(with Daniel Rogalski and James J. Zhang), Adv. Math.**264**(2014), 308--354.

[ PDF ] [ arXiv ] [ journal ] -
*Active lattices determine AW*-algebras*(with Chris Heunen), J. Math. Anal. Appl.**416**(2014), no. 1, 289--313.

[ PDF ] [ arXiv ] [ journal ] -
*Sheaves that fail to represent matrix rings*, in*Ring Theory and Its Applications*, Contemp. Math.**609**, 285--297, Amer. Math. Soc., Providence, RI, 2014.

[ PDF ] [arXiv ] [ journal ] -
*Diagonalizing matrices over AW*-algebras*(with Chris Heunen), J. Funct. Anal.**264**(2013), no. 8, 1873--1898.

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*Obstructing extensions of the functor Spec to noncommutative rings*, Israel J. Math.**192**(2012), no. 2, 667--698.

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*Noncommutative generalizations of theorems of Cohen and Kaplansky*, Algebr. Represent. Theory**15**(2012), no. 5, 933--975.

[ PDF ] [ arXiv ] [ journal ] -
*A one-sided Prime Ideal Principle for noncommutative rings*, Journal of Algebra and Its Applications**9**(2010), no. 6, 877--919.

[ PDF ] [ arXiv ] [ journal ] -
*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.

[ PDF ] [ journal ] -
*A Prime Ideal Principle in commutative algebra*(with T.Y. Lam), Journal of Algebra**319**(2008), no. 7., 3006--3027.

[ PDF ] [ journal ]

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.

Resources in noncommutative algebra:

- ncag.info (includes a list of upcoming conferences in noncommutative algebraic geometry)
- Women in Noncommutative Algebra and Representation Theory

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

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