# 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

Professor **Nils A. Baas**

Head of the Geometry & Topology Group

**Staff – Geometry & Topology Group**

**Members – Geometry & Topology Group**

## Research projects

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

## Recent Publications

Emilie Bjørlo Arentz-Hansen, Petter Andreas Bergh and Marius Thaule

**The morphism axiom for n-angulated categories**

*Theory and Applications of Categories*

Petter Andreas Bergh, Gustavo Jasso and Marius Thaule

**Higher n-angulations from local rings**

*Journal of the London Mathematical Society*

Elena Celledoni, Markus Eslitzbichler and Alexander Schmeding

**Shape analysis on Lie groups with application in computer animation**

*Journal of Geometric Mechanics (JGM)*

Daniel G. Davis and Gereon Quick

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

*Algebraic and Geometric Topology*

Alexander Schmeding and Christoph Wockel

**Functorial aspects of the reconstruction of Lie groupoids from their bisections**

*Journal of the Australian Mathematical Society*

Alexander Schmeding and Geir Bogfjellmo

**The tame Butcher group**

*Journal of Lie theory*

Alexander Schmeding, Geir Bogfjellmo and Rafael Dahmen

**Character groups of Hopf algebras as infinite-dimensional Lie groups**

*Annales de l'Institut Fourier*

Alexander Schmeding and Christoph Wockel

**(Re)constructing Lie groupoids from their bisections and applications to prequantisation**

*Differential geometry and its applications (Print)*

## Recent Visitors

- Dec 2015:
**Kathryn Hess Bellwald**(EPFL, Switzerland) - Dec 2015:
**Herbert Edelsbrunner**(IST, Austria) - Mar 2015:
**Ehud Meir**(Københavns Universitet) - Jan 2015:
**Frank Neumann**(University of Leicester) - Jan 2015:
**Chad Giusti**(University of Pennsylvania) - Nov 2014:
**Christoph Wockel**(Universität Hamburg) - Sep 2014:
**Rafael Dahmen**(Technische Universität Darmstadt) - Sep 2014:
**Helge Glöckner**(Universität Paderborn) - Sep 2014:
**Moritz Groth**(Radboud University Nijmegen)

## 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, 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** - Trondheim, 27–28 Nov 2008:
**Nordic Topology Meeting 2008** **Nordic Conference in Topology 2006**- Trondheim, 25–26 Nov 2004:
**The Topology Symposium 2004** **The Topology Symposium 2000****The Topology Symposium 1999****The Symposium in Algebraic K‑theory and Homotopy Theory 1998**