Associate Professor

Department of Mathematics

University of California, Irvine

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

Office: 510K Rowland Hall

CV

- Math 120A - Introduction to Abstract Algebra: Groups

My research focuses on ring theory (both noncommutative and commutative rings) and noncommutative geometry (including noncommutative algebraic geometry). I am often interested in situations where these ideas intersect with the study of category theory, operator algebras, and quantum physics.

Publications and preprints:*The domain and prime properties for Koszul rings and algebras*(with Daniel Rogalski).

[ PDF ] [ arXiv]*A tour of noncommutative spectral theories.*

[ PDF ]*Dual coalgebras of twisted tensor products*.

[ PDF ] [ arXiv ]*Categories of hypermagmas, hypergroups, and related hyperstructures*(with So Nakamura).

[ PDF ] [ arXiv ]*Contextuality and Kochen-Specker colorings of integer vectors*(with Ida Cortez).

[ PDF ] [ arXiv ]*The finite dual coalgebra as a quantization of the maximal spectrum*, J. Algebra**644**(2024), 287-328.

[ PDF ] [ arXiv ] [ journal ]-
*Graded twisted Calabi-Yau algebras are generalized Artin-Schelter regular*(with Daniel Rogalski, formerly titled*A twisted Calabi-Yau toolkit*), Nagoya Math. J.**245**(2022), 100-153.

[ PDF ] [ arXiv ] [ journal ] -
*Growth of graded twisted Calabi-Yau algebras*(with Daniel Rogalski), J. Algebra**539**(2019), 201-259.

[ PDF ] [ arXiv ] [ journal ] -
*Frobenius structures over Hilbert C*-modules*(with Chris Heunen), Comm. Math. Phys.**361**(2018), no. 2, 787-824.

[ PDF ] [ arXiv ] [ journal ] -
*On right S-Noetherian rings and S-Noetherian modules*(with Zehra Bilgin and Ünsal Tekir), Comm. Alg.**46**(2018), no. 2, 863-869.

[ PDF ] [ arXiv ] [ journal ] -
*Discretization of C*-algebras*(with Chris Heunen), J. Operator Theory**77**(2017), no. 1, 19-37.

[ PDF ] [ arXiv ] [ journal ] -
*A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors*(with Michael Ben-Zvi and Alexander Ma, and an appendix by Alexandru Chirvasitu), J. Algebra**491**(2017), 280-313.

[ PDF ] [ arXiv ] [ journal ] *Infinite-dimensional diagonalization and semisimplicity*(with Miodrag C. Ivanov and Zachary Mesyan), Israel J. Math.**215**(2016), no. 2, 801-855.

[ PDF ] [ arXiv ] [ journal ]*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), Trans. Amer. Math. Soc.**369**(2017), no. 1, 309-340.

[ 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.

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*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.

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

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*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: