# Geometry & topology

Our research in geometry and topology spans problems ranging from fundamental curiosity-driven research on the structure of abstract spaces to computational methods for a broad range of practical issues such as the analysis of the shapes of big data sets.

The members of the group are all embedded into a network of international contacts and collaborations, aim to produce science and scientists of the highest international standards, and also contribute to the education of future teachers.

## About geometry and topology

**Geometry** has always been tied closely to mathematical physics via the theory of differential equations. It uses curvature to distinguish straight lines from circles, and measures symmetries of spaces in terms of Lie groups, named after the famous Norwegian mathematician Sophus Lie.

**Topology**, in contrast, is the study of qualitative properties of spaces that are preserved under continuous deformations. The spaces in question can be tame like a smooth manifold, or wild and hard as rock.

Topological ideas arise in practical problems, and research in topology still finds new applications, in particular to mathematical problems that are not directly phrased in terms of numbers and functions.

**Homotopy theory** (a subdiscipline of topology) has many applications within mathematics itself, in particular to algebra and number theory.

## Contact

Associate Professor **Gereon Quick**

Head of the geometry & topology group

## Selected publications

**Nils Andreas Baas**, NC Seeman and Andrew Stacey

**Synthesising topological links**

*Journal of Mathematical Chemistry*

**Petter Andreas Bergh**, Gustavo Jasso and **Marius Thaule**

**Higher n-angulations from local rings**

*Journal of the London Mathematical Society*

Daniel G. Davis and **Gereon Quick**

**Profinite and discrete G-spectra and iterated homotopy fixed points**

*Algebraic and Geometric Topology*

Ehud Meir and **Markus Szymik**

**Drinfeld centers for bicategories**

*Documenta Mathematica*

Pedro de M. Rios and **Eldar Straume**

**Symbol Correspondences for Spin Systems**

*Birkhäuser Basel*

## Projects

Gereon Quick and Markus Szymik collaborate in **Motivic Hopf equations**, a project supported by the Research Council of Norway.

## Partners

The group members collaborate with people from

- Aarhus Universitet
- Courant Institute, New York University
- Harvard University
- Institute for Advanced Study (IAS), Princeton
- Københavns Universitet
- Massachusetts Institute of Technology (MIT)
- New York University (NYU)
- Stanford University
- University of California, Berkeley
- University of California, Davis
- University of São Paulo, Sao Carlos

## Seminars and conferences

### Seminars

- Topology & Geometry Seminar: Upcoming seminars plus archives

### Conferences

- Trondheim, 30 Nov–2 Dec 2016:

**Topology and Applications** - Trondheim, 3–4 Nov 2016:

**Geometry and Lie theory. Applications to classical and quantum mechanics** - Trondheim, 27–28 Nov 2014:

**Nordic Topology Meeting 2014** - Trondheim, 5–6 Dec 2011:

**Norwegian Topology Meeting 2011** - Aug 18–19, 2008:

**Conference on Systems Biology and Disease** - Geiranger, Norway, Aug 12–16, 2008:

**Workshop on Genes, Genomes and Evolution: Structure and Hyperstructure**