I recently obtained my PhD in algebraic topology under the direction of Ib Madsen, and
I will be a Postdoc in Copenhagen until August 2013.
My research is divided into two subjects. My primary interest is to develop trace methods for the study of K-theory of categories with duality. In my PhD thesis, I study an equivariant version of topological Hochschild homology for these categories. In the main result I show that this theory for rings with antistructures is equivariantly equivalent to a stabilized K-theory.
I am also interested in relative h-principles. When David Ayala was a Postdoc in Copenhagen, he supervised a research project where I proved a relative h-principle for certain topological sheaves. These sheaves have structural properties similar to a sheaf involved in the study of the homotopy type of cobordism categories. The techniques used in the proof are of categorical and simplicial nature. One of the main ingredients is a Quillen theorem B applied to a functor between cobordism categories.
Department of Mathematical Sciences
2100 København Ø
PhD Thesis Stable real K-theory and real topological Hochschild homology.
Preprint A relative h-principle via cobordism-like categories.
Master Thesis A Survey of Index Theory and a Calculation of the Truncated Equivariant Witten Genus.
Research Statement here.