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 120B, Rings and Fields

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

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:*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*.

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*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.

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

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

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

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

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*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.

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

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*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.

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

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*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.

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

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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: