Department of Mathematics
Email: reyes@bowdoin (where "bowdoin" means "bowdoin dot edu")
Office: 104 Searles Science Building
Office Hours (Fall 2015): by appointment (I am on teaching leave until the Spring 2016 semester)
Here is my CV
if you are interested.
Manny's Research and Papers
My research interests lie in Ring Theory (both noncommutative and commutative rings)
and Noncommutative Geometry (including noncommutative algebraic geometry).
I am also interested in cases where these ideas intersect with the study of category theory,
operator algebras, and quantum physics.
Here are some preprints of my
- A Kochen-Specker theorem for integer matrices and noncommutative spectrum functors
(with Michael Ben-Zvi and Alexander Ma, and an appendix by Alexandru Chirvasitu),
(Also available at arXiv:1509.03618.)
- Infinite-dimensional diagonalization and semisimplicity
(with Miodrag C. Ivanov and Zachary Mesyan), submitted.
(Also available at arXiv:1502.05184.)
- A prime ideal principle for two-sided ideals,
to appear in Communications in Algebra.
(Also available at arXiv:1501.06808.)
- On discretization of C*-algebras
(with Chris Heunen), submitted.
(Also available at arXiv:1412.1721.)
- Skew Calabi-Yau
triangulated categories and Frobenius Ext-algebras
(with Daniel Rogalski and James J. Zhang), to appear in Transactions of the AMS.
(Also available at arXiv:1408.0536.)
- Quantum theory realizes
all joint measurability graphs (with Chris Heunen and Tobias Fritz),
Phys. Rev. A. 89 (2014), no. 3, 032121.
(Also available at arXiv:1310.3698.)
- Skew Calabi-Yau algebras
and homological identities (with Daniel Rogalski and James J. Zhang),
Adv. Math. 264 (2014), 308--354.
(Also available at arXiv:1302.0437.)
- Active lattices determine
AW*-algebras (with Chris Heunen),
J. Math. Anal. Appl. 416 (2014), no. 1, 289--313.
(Also available at arXiv:1212.5778.)
- Sheaves that fail to represent
matrix rings, in Ring Theory and Its Applications, Contemp.
Math. 609, 285--297, Amer. Math. Soc., Providence, RI, 2014.
(Also available at arXiv:1211.4005.)
- Diagonalizing matrices over AW*-algebras
(with Chris Heunen), J. Funct. Anal. 264 (2013), no. 8, 1873--1898.
(Also available at arXiv:1208.5120.)
- Obstructing extensions of the functor Spec to
noncommutative rings, Israel J. Math. 192 (2012), no. 2, 667--698.
(Also available at arXiv:1101.2239.)
generalizations of theorems of Cohen and Kaplansky, Algebr. Represent. Theory 15
(2012), no. 5, 933--975.
(Also available at arXiv:1007.3701.)
one-sided Prime Ideal Principle for noncommutative rings, Journal of Algebra and Its
Applications 9 (2010), no. 6, 877--919.
(Also available at arXiv:0903.5295.)
- 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.
- A Prime Ideal
Principle in commutative algebra (with T.Y. Lam), Journal of Algebra 319 (2008), no. 7., 3006--3027.
Here are some slides from selected talks that I have given:
Related to my research interests:
Some websites where I like to answer, ask, and read mathematics questions:
Here are some links to Wikipedia pages that concern various aspects of my work: