INTERDISCIPLINARY STOCHASTIC PROCESSES COLLOQUIUM Tuesday January 21, 4.10 - 5.00pm, room 60 Evans Speaker: Olle Haggstrom Title: Uniqueness (and non-uniqueness) of the infinite cluster in percolation models. Abstract: One of the most important and celebrated theorems in percolation theory is the uniqueness of the infinite cluster for i.i.d. percolation on Z^d. Although this result dates back to the late 1980's, the issue of uniqueness of infinite clusters is still very much alive as a research area. For instance, what happens when we move to various types of dependent models, or to other lattices? And what happens if we focus not on connected components, but instead on entangled components, or on rigid components? In this talk I plan to give an introduction to these topics, and give a brief survey of known results and open problems.