Manuel Reyes



Assistant Professor
Department of Mathematics
Bowdoin College

Email: reyes@bowdoin (where "bowdoin" means "bowdoin dot edu")
Office: 104 Searles Science Building
Office Hours (Fall 2017): TBA
Phone: 207-725-3574

Here is my CV, which is updated irregularly.


Spring 2017 Courses

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


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 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:
  1. Frobenius structures over Hilbert C*-modules (with Chris Heunen), submitted.
    [ PDF ]   [ arXiv ]  
  2. Right S-noetherian rings (with Zehra Bilgin and Ünsal Tekir), to appear in Comm. Alg.
    [ PDF ]   [ arXiv ]   [ journal ]
  3. Discretization of C*-algebras (with Chris Heunen), J. Operator Theory 77 (2017), no. 1, 19-37.
    [ PDF ]   [ arXiv ]   [ journal ]
  4. 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 ]
  5. Infinite-dimensional diagonalization and semisimplicity (with Miodrag C. Ivanov and Zachary Mesyan), Israel J. Math. 215 (2016), no. 2, 801-855.
    [ PDF ]   [ arXiv ]   [ journal ]
  6. A prime ideal principle for two-sided ideals, Comm. Alg. 44 (2016), no. 11, 4585-4608.
    [ PDF ]   [ arXiv ]   [ journal ]
  7. 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 ]
  8. Quantum theory realizes all joint measurability graphs (with Chris Heunen and Tobias Fritz), Phys. Rev. A. 89 (2014), no. 3, 032121.
    [ PDF ]   [ arXiv ]   [ journal ]
  9. Skew Calabi-Yau algebras and homological identities (with Daniel Rogalski and James J. Zhang), Adv. Math. 264 (2014), 308--354.
    [ PDF ]   [ arXiv ]   [ journal ]
  10. Active lattices determine AW*-algebras (with Chris Heunen), J. Math. Anal. Appl. 416 (2014), no. 1, 289--313.
    [ PDF ]   [ arXiv ]   [ journal ]
  11. 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 ]
  12. Diagonalizing matrices over AW*-algebras (with Chris Heunen), J. Funct. Anal. 264 (2013), no. 8, 1873--1898.
    [ PDF ]   [ arXiv ]   [ journal ]
  13. Obstructing extensions of the functor Spec to noncommutative rings, Israel J. Math. 192 (2012), no. 2, 667--698.
    [ PDF ]   [ arXiv ]   [ journal ]
  14. Noncommutative generalizations of theorems of Cohen and Kaplansky, Algebr. Represent. Theory 15 (2012), no. 5, 933--975.
    [ PDF ]   [ arXiv ]   [ journal ]
  15. A one-sided Prime Ideal Principle for noncommutative rings, Journal of Algebra and Its Applications 9 (2010), no. 6, 877--919.
    [ PDF ]   [ arXiv ]   [ journal ]
  16. 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 ]
  17. 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: