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** Oslo Symposium of the Topology Group **Thursday, 26th Februar 2015, 2 p.m. in room 32/107

#### Simen Lønsethagen (Universität Oslo)

##### Brown representability for equivariant motivic homotopy theory

In the talk I will present a proof for Brown representability for equivariant motivic homotopy theory. The equivariant Nisnevich topology and motivic model structures will be discussed. The proof follows the arguments of Naumann and Spitzweck in the non-equivariant case.

#### Håkon Andreas Kolderup (Universität Oslo)

##### K_{2} and quadratic reciprocity

We discuss the result of Tate on the structure of the group K_2(Q) and how this is connected to the quadratic reciprocity law.

#### Jonas Irgens Kylling (Universität Oslo)

##### Hermitian K-theory of finite fields and the motivic Adams spectral sequence

The aim of the talk is to compute the two component of Hermitian K-theory of finite fields in odd characteristic. This will be accomplished by use of the motivic Adams spectral sequence for a spectrum representing Hermitian K-Theory (Jens Hornbostel, 2005). The work is similar to work by Kyle M. Ormsby, 2011 and Michael A. Hill, 2011.

#### Peter Arndt (Universität Regensburg)

##### Models for infinity categorical algebra

Given a cartesian closed presentable infinity category and an algebraic structure (in the sense of Lawvere theories) therein, we produce a model category and and an algebraic structure which serve as a presentation of their infinity categorical counterparts.

#### Dr. Utsav Choudhury (Universität Osnabrück)

##### Presheaves of unbounded chain complexes on a Grothendieck site

The main goal of the talk will be to discuss the following two results

1. Given a small category *T* and let *V* be the category of unbounded chain complexes, the category of presheaves of unbounded chain complexes on *T* with the projective model structure is the universal *V*-enriched model category.

2. If *T* is equipped with Grothendieck topology τ, then a presheaf of unbounded chain complexes is fibrant in the τ-local model structure if and only if it satisfies τ-descent.

#### Hadrian Heine (Universität Osnabrück)

##### A characterization of cellular motivic spectra by *E*-infinity modules

In my talk I describe how to model cellular motivic spectra by *E*-infinity modules in *QS*^{0}-diagrams in topological spectra.