Department of Mathematics
Email: reyes@bowdoin (where "bowdoin" means "bowdoin dot edu").
Office: 104 Searles Science Building.
Office Hours (Fall 2014): by appointment.
You can see my CV
if you are interested.
Fall 2014 Courses
I am on leave for the 2014-2015 academic year.
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
- Skew Calabi-Yau
triangulated categories and Frobenius Ext-algebras
(with Daniel Rogalski and James J. Zhang), submitted.
(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:
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: