Dr. Timothy Ford

Education

• Ph.D. in Mathematics, Department of Mathematics, Colorado State University, 1980.

Research Interests

• Mathematics Subject Classification 14F22, 16K50, 16H05, 14F20
• The Brauer group of a commutative ring, the Brauer group of a variety
• Azumaya algebras defined over the function field of a variety
• étale cohomology
• Commutative algebra and algebraic geometry 

Research Description

My research involves that area of Algebra where Ring Theory, Commutative Algebra and Algebraic Geometry overlap. The main focus is the Brauer group of a commutative ring, which classifies the Azumaya algebras. The rings that arise are rings of functions defined on algebraic varieties. This study employs many methods from all areas of Algebra. There are essential connections with the theory of separable algebras, Morita theory, the theory of faithfully flat descent, Galois theory, cohomology, derivations, differentials, reflexive lattices, maximal orders and class groups.

Recent Publications

[1] The Brauer group of an affine double plane associated to a hyperelliptic curve, Comm. Algebra. 45 (2017) pp. 1416-1442.

[2] The relative Brauer group and generalized cyclic crossed products for a ramified covering, J. Algebra 450 (2016) pp. 1–58.

[3] Separable Algebras, Graduate Studies in Mathematics, Vol. 183, The American Mathematical Society, Providence, RI, 2017, 658 pages.

[4] A Family of Nonnormal Double Planes Associated to Hyperelliptic Curves, in Algebraic Curves and Applications, vol. 724 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2019, pp. 45–54.

[5] Introduction to Abstract Algebra, AMS Open Math Notes, Reference #

OMN:202006.110827, 2024. An algebra book containing an introduction to group

theory, ring theory, linear algebra, and fields, 350 pages. Based on my notes for the two semester course: Introduction to Abstract Algebra. Freely available as a pdf file at: https://www.ams.org/open-math-notes/omn-view-listing?listingId=110827

Work in Progress

[1] Commutative Algebra, 527 pages. An algebra book providing a self-contained introduction to the theory of commutative algebra. Accessible to students who have completed a standard first course in abstract algebra. The latest version is available as a pdf file at:
https://tim4datfau.github.io/Timothy-Ford-at-FAU/preprints/CA.pdf.

Scholarly Activities

Being a mathematical fanatic, I never stop working. I'm doing math 24 hours a day, 7 days a week.  

Personal Website

https://tim4datfau.github.io/Timothy-Ford-at-FAU/