Manuel Reyes



Associate Professor
Department of Mathematics
University of California, Irvine

Email: manny.reyes@uci (where "uci" means "uci dot edu")
Office: 510K Rowland Hall
CV

Fall 2024 teaching

Manny's Research and Papers

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:
  1. The domain and prime properties for Koszul rings and algebras (with Daniel Rogalski).
    [ PDF ]   [ arXiv]  
  2. A tour of noncommutative spectral theories.
    [ PDF ]  
  3. Dual coalgebras of twisted tensor products.
    [ PDF ]   [ arXiv ]  
  4. Categories of hypermagmas, hypergroups, and related hyperstructures (with So Nakamura).
    [ PDF ]   [ arXiv ]  
  5. Contextuality and Kochen-Specker colorings of integer vectors (with Ida Cortez).
    [ PDF ]   [ arXiv ]  
  6. The finite dual coalgebra as a quantization of the maximal spectrum, J. Algebra 644 (2024), 287-328.
    [ PDF ]   [ arXiv ]   [ journal ]
  7. 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 ]
  8. Growth of graded twisted Calabi-Yau algebras (with Daniel Rogalski), J. Algebra 539 (2019), 201-259.
    [ PDF ]   [ arXiv ]   [ journal ]
  9. Frobenius structures over Hilbert C*-modules (with Chris Heunen), Comm. Math. Phys. 361 (2018), no. 2, 787-824.
    [ PDF ]   [ arXiv ]   [ journal ]
  10. 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 ]
  11. Discretization of C*-algebras (with Chris Heunen), J. Operator Theory 77 (2017), no. 1, 19-37.
    [ PDF ]   [ arXiv ]   [ journal ]
  12. 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 ]
  13. Infinite-dimensional diagonalization and semisimplicity (with Miodrag C. Ivanov and Zachary Mesyan), Israel J. Math. 215 (2016), no. 2, 801-855.
    [ PDF ]   [ arXiv ]   [ journal ]
  14. A prime ideal principle for two-sided ideals, Comm. Alg. 44 (2016), no. 11, 4585-4608.
    [ PDF ]   [ arXiv ]   [ journal ]
  15. 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 ]
  16. Quantum theory realizes all joint measurability graphs (with Chris Heunen and Tobias Fritz), Phys. Rev. A. 89 (2014), no. 3, 032121.
    [ PDF ]   [ arXiv ]   [ journal ]
  17. Skew Calabi-Yau algebras and homological identities (with Daniel Rogalski and James J. Zhang), Adv. Math. 264 (2014), 308-354.
    [ PDF ]   [ arXiv ]   [ journal ]
  18. Active lattices determine AW*-algebras (with Chris Heunen), J. Math. Anal. Appl. 416 (2014), no. 1, 289-313.
    [ PDF ]   [ arXiv ]   [ journal ]
  19. 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 ]
  20. Diagonalizing matrices over AW*-algebras (with Chris Heunen), J. Funct. Anal. 264 (2013), no. 8, 1873-1898.
    [ PDF ]   [ arXiv ]   [ journal ]
  21. Obstructing extensions of the functor Spec to noncommutative rings, Israel J. Math. 192 (2012), no. 2, 667-698.
    [ PDF ]   [ arXiv ]   [ journal ]
  22. Noncommutative generalizations of theorems of Cohen and Kaplansky, Algebr. Represent. Theory 15 (2012), no. 5, 933-975.
    [ PDF ]   [ arXiv ]   [ journal ]
  23. A one-sided Prime Ideal Principle for noncommutative rings, Journal of Algebra and Its Applications 9 (2010), no. 6, 877-919.
    [ PDF ]   [ arXiv ]   [ journal ]
  24. 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 ]
  25. 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:

Links

Resources in noncommutative algebra:

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: