Research Interests
Cohomological Methods for Projective Homogeneous Varieties
The study of cohomological invariants of algebraic varieties or schemes has led to the solution of many classical algebraic and geometric problems. An active subject of investigation is the geometry of a linear, or reductive, algebraic group G and its action on a projective variety X. In my current research, I apply cohomological methods to study the geometry of algebraic objects endowed with a transitive group action. In particular, I focus on Grothendieck's K_0 of such varieties, and the associated gamma filtration.
An Analogue to the Gauss Class Number Problem
Another project on which I have worked begins by replacing the ideal class group of a number field F with the motivic wild kernel of F, a motivic cohomology group of the ring of integers of F. This gives rise to an analogue to the classical Gauss problem of determining all imaginary quadratic number fields having class number 1. Under the assumption of the main conjecture of Iwasawa theory, I was able to use the special values of the Dedekind zeta function in combination with a set of discriminant bounds given by Odlyzko to characterize all totally real number fields having trivial motivic wild kernel.
The study of cohomological invariants of algebraic varieties or schemes has led to the solution of many classical algebraic and geometric problems. An active subject of investigation is the geometry of a linear, or reductive, algebraic group G and its action on a projective variety X. In my current research, I apply cohomological methods to study the geometry of algebraic objects endowed with a transitive group action. In particular, I focus on Grothendieck's K_0 of such varieties, and the associated gamma filtration.
An Analogue to the Gauss Class Number Problem
Another project on which I have worked begins by replacing the ideal class group of a number field F with the motivic wild kernel of F, a motivic cohomology group of the ring of integers of F. This gives rise to an analogue to the classical Gauss problem of determining all imaginary quadratic number fields having class number 1. Under the assumption of the main conjecture of Iwasawa theory, I was able to use the special values of the Dedekind zeta function in combination with a set of discriminant bounds given by Odlyzko to characterize all totally real number fields having trivial motivic wild kernel.
