I am a PhD student in mathematics at University of Copenhagen, and part of
the Center for Symmetry and Deformation.
I work within the field of topology under the supervision of Ib Madsen and I
expect to graduate in December 2012.
My interests are divided in two subjects. The first project I worked on,
was about h-principles with boundary conditions, under the supervision of
David Ayala.
Given a topological spaces valued sheaf on the category of manifolds and embeddings, there is a map from it to a new sheaf.
The weak homotopy type of the new sheaf evaluated on a manifold is generally easier to compute than
the original one. Gromov found sufficient conditions on the original sheaf so that this map is a weak equivalence
on a certain class of manifolds. I used simplicial categories techniques coming from the study of
the weak homotopy type of the cobordism categories to determine if this map restricted and corestricted
to elements having a prescribed behaviour on the boundary is still a weak equivalence.
Now I am working on real algebraic K-theory. This is a spectrum with involution associated to a ring (spectrum) with an antistructure. I am interest in the fiber of the map in K-theory induced by a well behaving ring map. The methods I am using (trace maps) compare this fiber with the fiber of the map induced in a gadget called real topological cyclic homology, where computations are easier. The case without involution has been solved by McCarthy and Dundas, and I am trying to generalize their result in this equivariant setting.
Address
Department of Mathematical Sciences
Universitetsparken 5
2100 København Ø
Denmark
Email
dotto@math.ku.dk
Preprint An H-principle With Boundary Condition.
Master Thesis A Survey of Index Theory and a Calculation of the Truncated Equivariant Witten Genus.
CV here.