To participate in this seminar, please register HERE.

In this talk, I will (try to) give a mini introduction to reflection positivity and use it to show that the XY-model undergoes an order-disorder phase transition on the three dimensional lattice. This is in stark contrast to the two dimensional case, where the model is never ordered. The main goal of this talk is to prove the so called ‘’Gaussian domination'’ and, time permitting, the phase transition. I will introduce all the relevant terminology during the talk.