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## WS 2018/2019

### 23.10.2018 um 14:15 Uhr in 69/117:

#### Maria Yakerson (Universität Duisburg-Essen)

##### How to encode transfers in motivic homotopy theory

Voevodsky’s approach to constructing the (derived) category of motives starts with introducing so called presheaves with transfers. Later Calmès and Fasel added extra data of quadratic forms to this construction, by considering presheaves with Milnor-Witt transfers. We will show that these transfers are examples of a more general construction of *E*-transfers, defined for any motivic ring spectrum *E*. We will also discuss relation of *E*-transfers with framed transfers, and some consequences for understanding the category of *E*-modules.

This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo

### 06.11.2018 um 14:15 Uhr in 69/117:

#### Elmiro Vetere (Universität Freiburg)

##### Quasi-coherent cohomology of log schemes

This talk will be about the cohomological aspects of Logarithmic geometry. We will define the Kummer log etale site and the (full) log etale site and we will compare their cohomologies to classical etale cohomology, for schemes of finite type over ℂ. We will also talk about log blow-ups, log regularity and how rational singularities appear in this context.

### 13.11.2018 um 14:15 Uhr in 69/117:

#### Ilia Pirashvili (Universität Osnabrück)

##### Axiomatisation of the (étale) fundamental groupoid

The Galois group and the Poincaré group, which were unified by the works of Grothendieck, are of course very imporant invariants. However, it's difficult to state 'what's so special about them'. Indeed, there exists no axiomatic definition of the fundamental group.

In this talk, we will discuss something very closely related. Namely, the universal property of the fundamental groupoid. The latter can be thought of as a 'simultanious collection of fundamental groups at every connected component'. We will give an axiomatisation of the fundamental groupoid (both topological and étale if time permits) using the Seifer-van Kampen theorem, and tools from 2-category theory.

We will finially discuss some of the implications of these results, both from a conceptual- as well as calculatory viewpoint.

### 11.12.2018 um 14:15 Uhr in 69/117:

#### Viktor Tabakov (Freie Universität Berlin)

##### Milnor-Witt *K*-theory of finite fields

The main goal of the talk will be the computation of Milnor-Witt *K*-theory of a finite field when the characteristic is not equal to 2. This can be done by generalizing the proof for Milnor *K*-theory, which also will be given in the talk. If time permits, we will discuss necessary parts of the theory of quadratic forms over a field.

### 08.01.2019 um 14:15 Uhr in Raum 69/E15

#### Markus Spitzweck (Universität Osnabrück)

##### Infinity categories with genuine duality

Hermitian K-theory and L-theory can be defined for various notions of quadratic structure, e.g. using symmetric bilinear forms or quadratic forms (which are not the same when 2 is not invertible in the ground ring).

We will define a structure on an infinity category called a genuine duality which will then serve as input for a suitable definition of hermitian K-theorytaking care of such refinements.We will compare different models for that structure.

This is joint work in progress with Hadrian Heine and Paula Verdugo.

### 22.01.2019 um 14:15 Uhr in 69/117:

#### Anand Sawant (LMU München)

##### Cellular *A*^{1}-homology

^{1}

We will introduce a new version of *A ^{1}*-homology, which is often entirely computable. We will describe some explicit computations of these homology groups for classifying spaces, reductive groups and generalized flag varieties and also discuss some applications. The talk is based on joint work with Fabien Morel.

### 29.01.2019 um 14:15 Uhr in 69/117:

#### Achim Krause (Universität Münster)

##### Cellular *p*-complete motivic homotopy theory over **C** via filtered spectra

**C**

In this talk I want to explain recent work with Isaksen, Gheorghe and Ricka on a purely homotopy theoretic description for the structure of the category of *p*-complete cellular spectra over *C*, based on earlier observations by Isaksen on the structure of the motivic Adams-Novikov spectral sequence. This description naturally produces the correct motivic analogues of many classical spectra, such as Eilenberg-MacLane spectra or *K*-theory spectra. As an exciting application, we obtain a new motivic analogue of tmf.