### Project 12: "Exchange graphs of triangulations"

*This project is running since 2015.*

Principal investigator: Karin Baur

University of Graz, Austria.

*Mentor for*: Oh.

### DK Student

**Second phase of the doctoral program:****Lukas Andritsch**(Austria; since October 2015)

*Email*: lukas.andritsch@edu.uni-graz.at

*Mentors*: Oswin Aichholzer, Daniel Smertnig.

### Associated Students

**Second phase of the doctoral program:****Jordan McMahon**(New Zealand; since October 2015)

*Email*: jordan.mcmahon@uni-graz.at

*Mentors*: Alfred Geroldinger, Dusko Bogdanic.**Hannah Vogel**(USA; February 2013 - September 2016)

*Email*: hannah.vogel@uni-graz.at

*Mentors*: Michael Kerber, Birgit Vogtenhuber.

*PhD Defense*: September 08, 2016.

*Referees*: K. Baur, A. Felikson (Durham)

*Examiners*: K. Baur, A. Felikson (Durham)

### Project description (pdf-file)

Research interests of Karin Baur lie in combinatorial and geometric aspects of representation theory. In the present project she considers interactions of geometrical objects and categories of representations. Of particular importance are arcs and triangulations in Riemann surfaces with marked points. Each (oriented) arc corresponds to an indecomposable object in the associated module or cluster category. Algebraic properties of the categories are reflected by the geometric properties (e.g. dimension of Ext spaces are given by crossing numbers). One of the goals of Baur's research is to develop a general theory of surface categories and thus to provide a novel combinatorial geometric approach to representation-theoretic categories.