Date: Tuesday, March 25, 2014
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Speaker: Brittan Farmer
Abstract: We are all familiar with materials which have a crystalline phase at low temperature. An example we have seen a lot this winter is ice – the crystalline phase of water. I will present the article “A Proof of Crystallization in Two Dimensions” by Florian Theil. In this article, Theil analyzes a model of particle systems in two dimensions with pairwise interaction energy. He shows that the minimum energy per particle of such a system converges to an explicit constant. Under suitable boundary conditions, the minimizers form a triangular lattice – a crystal structure! I will present these results from the aforementioned article and explain some of the ingredients of the proof.