|Phone:||+1 (518) 442-4639|
|Fax:||+1 (518) 442-4731|
Research interests: algebraic and geometric topology, algebraic K-theory and L-theory.
Before joining the University at Albany in 2010, I was a visiting assistant professor at Binghamton University, SUNY, since 2006. Until then I was in the topology group at the Westfälische Wilhelms-Universität Münster (Germany), where I finished my doctorate under the supervision of Wolfgang Lück.
Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought.
Office hours: MWF 9:20–10:15
Office hours: MTW 4:05–5:00
Office hours: MWF 8:15–9:15
Office hours: TuThM 8:45–10:05 and Tu 1:15–2:35
Office hours: M 2:45–5:35 and W 2:45–4:05
Office hours: MWF 11:30–12:30
Office hours: M 1:30–2:30 and WF 10:30–11:30
Office hours: MW 11:00–12:30
Office hours: MW 3:30–5:00
Office hours: MTWRF 11:20–12:20
Office hours: MW 3:00–4:30
Office hours: MWF 3:30–4:30
Office hours: MW 2:30–4:00
Office hours: MWF 1:10–2:10
Office hours: MW 3:00–4:30
Office hours: W 2:30–4:00 and R 10:00-11:30
We use topological cyclic homology and the cyclotomic trace to detect elements in the rationalized higher algebraic K-theory groups of integral group rings. Modulo a deep conjecture in number theory, the so-called Schneider conjecture, and under mild homological finiteness conditions on the group, we prove that the connective algebraic K-theory assembly map for the family of virtually cyclic subgroups is rationally injective. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand inside the algebraic K-theory groups of an integral group ring in terms of group homology. Along the way we also prove integral splitting and isomorphism results for THH- and TC-assembly maps with coefficients in arbitrary connective ring spectra.
In general the processes of taking a homotopy inverse limit of a diagram of spectra and smashing spectra with a fixed space do not commute. In this paper we investigate under what additional assumptions these two processes do commute. In fact we deal with an equivariant generalization which involves spectra and smash products over the orbit category of a discrete group. Such a situation naturally occurs if one studies the equivariant homology theory associated to topological cyclic homology. The main theorem of this paper will play a role in the generalization of the results obtained by Bökstedt, Hsiang and Madsen about the algebraic K-theory Novikov Conjecture to the assembly map for the family of virtually cyclic subgroups.
The classical Witt groups of quadratic forms have been generalized in algebraic topology, with Wall’s and Ranicki’s L-groups for surgery theory, and in algebraic geometry, with Knebusch’s Witt groups of schemes and Balmer’s Witt groups of triangulated categories with duality. We introduce algebraic L-theory groups for so-called pre-triangulated differential graded categories with duality, generalizing and unifying the two aforementioned approaches.