June - August 2010
Three main categories of topics will be considered:
- Algebraic Study of Graphs: Constructing infinite families with specific properties.
- Precise foundations: The `right' definition of graphs and maps
- Natural constructions of new graphs from old.
- Linear Algebra on graphs and its connections with homology.
- Famous families of graphs and their properties (with some new twists).
- Heat Kernels on Graphs: Asymptotic properties of graphs.
- Combinatorial Laplacian and Heat Kernels.
- Connection between algebraic properties of groups and properties of the
heat kernels of their Cayley graphs.
- The free group on two generators and its Laplacian.
- Free products of groups and their Laplacians.
- Graphs and Groupoids: Extension of graph-theoretic ideas to other research areas.
- Groupoids coming from directed graphs; Cuntz-Krieger type structures.
- Possible applications to tilings and (quasi-)crystals.
- Fundamental groupoid of a topological space.
- Groupoids associated to foliations.
The participants should devote their full time to the program and not
engage in any other course work or employment during the program.