The purpose of these four lectures is to provide an introduction to the theory of dg-
categories. There are several possible points of view to present the subject, and my choice …

Let G be a finite group. We give Quillen equivalent models for the category of G-spectra as
categories of spectrally enriched functors from explicitly described domain categories to …

The homotopy limit problem for Karoubiʼs Hermitian K-theory (Karoubi, 1980)[26] was
posed by Thomason (1983)[44]. There is a canonical map from algebraic Hermitian K-theory …

Topological Hochschild homology (THH) of a “ring up to homotopy” has, after its existence
and even some calculations had been conjectured by Goodwillie in the 1980's, appeared in …

The seminar focuses on a recent solution, by the authors, of a long standing problem
concerning the stable module category (of not necessarily finite dimensional …

We describe an iterable construction of THH for an E n ring spectrum. The reduced version
is an iterable bar construction and its n th iterate gives a model for the shifted cotangent …

We show that the category of free rational G-spectra for a connected compact Lie group G is
Quillen equivalent to the category of torsion differential graded modules over the polynomial …

We interpret different constructions of the algebraic K‐theory of spaces as an instance of
derived Koszul (or bar) duality and also as an instance of Morita equivalence. We relate the …

In this paper we analyse the higher topological Hochschild homology of commutative Thom
S-algebras. This includes the case of the classical cobordism spectra MO, MSO, MU, etc. We …

Monoidality of Franke's exotic model Page 1 Advances in Mathematics 228 (2011) 3223–3248
www.elsevier.com/locate/aim Monoidality of Franke’s exotic model David Barnesa,1,3 …