Title #1: Enumeration of perfect matchings of cellular graphs

Abstract:
A graph is cellular if it is bipartite, its edges can be partitioned into 4-cycles and its vertices all have degree 2 or 4. Using alternating sign patterns, Mihai Ciucu proved in 1996 that the number of matchings of such a graph is a power of 2 (which can be easily read off the graph) times the number of matchings of the graph we obtain by deleting all vertices of degree 2. I will present a slightly generalised version of this theorem and prove it using the same ideas as Ciucu does. Finally, I will present the classical application (also done by Ciucu) of this theorem, namely the enumeration of domino tilings of the Aztec Diamond.

Title #2: Background to the Razumov-Stroganov (Ex-)Conjecture

Abstract:
Fully packed loops are certain finite subgraphs of the Z^{^2}-grid. One
wouldn't expect to find parallels to an infinite mathematical object
like a tiling of a semi-infinite cylinder. In this talk we will learn
about some properties of the two objects and use probability theory to
see that they are comparable when talking about noncrossing matchings.