Danny Krashen

Using shapes to understand the arithmetic of algebraic structures.

I am an associate professor of mathematics at the University of Georgia, Athens. My research is currently supported by an NSF CAREER grant "The Arithmetic of Fields and the Complexity of Algebraic Structures," for which I was awarded a Presendential Early Career Award (PECASE). My research is also support by NSF FRG grant "Obstructions to Local-Global Principles and Applications to Algebraic Structures," and I am a co-PI on the UGA RTG grant "Algebra, Algebraic Geometry, and Number Theory." I have been awarded the University of Georgia Creative Research Medal, and the University of Georgia Outstanding Professor Award. Recently, I have been invited to be a fellow of the American Mathematical Society.

Research Interests:

Finite dimensional division algebras and the Brauer group, linear algebraic groups, algebraic cycles, and field theory.

I am particularly interested in the use of techniques and ideas from algebraic topology and algebraic geometry to problems in algebra.