I am mainly interested in algebraic geometry. In particular, I study cycles, motives and motivic cohomology.
On December 12th 2003 I succesfully defended my dissertation and therefore since January 2004 I have a Ph.D. in Mathematics from Rutgers University. The title of the dissertation is “Schur functors and motives”.
Since 2000, I’ve been working with V. Voevodsky and C. Weibel on writing the lecture notes for a series of lectures given by V. Voevodsky during Fall 1999 and Spring 2000 at the Institute for Advanced Study in Princeton, NJ. The book “Lecture notes on motivic cohomology” was (finally) published on September 2006 as the second volume of the Clay Mathematics Monographs by the American Mathematical Society in 2006.
Since 2003 I have been working on a generalization of a finiteness notion introduced independently by Kimura and O’Sullivan. Kimura introduced this notion to study the properties of the categories of (classical) motives. In particular, the finiteness of the motive of a smooth projective surface with p_g=0 implies that the zero cycles are representable (Bloch’s conjecture). I introduced a different finiteness (Schur-finiteness), inspidred by an article of Deligne. The Schur-finiteness is more general notion but it behaves better with respect to the triangulated structure of the category of motives DM introduced by Voevodsky. In the effort to generalize the result by Kimura, one is faced with problems related to trace identities and the combinatorial structure of Schur polynomials.