TALK 1:SPEAKER: Naomi FeldheimTITLE: Gap probabilities for zeroes of stationary Gaussian functionsABSTRACT:We consider real stationary Gaussian functions on the real axis and discuss the 'gap probability' (i.e., the probabilitythat the function has no zeroes in [0,T]). We give sufficient conditions for this probability to be roughly exponential in T.(Joint work with Ohad Feldheim).
SPEAKER: Ohad Feldheim
TITLE: Rigidity of 3-colorings of the d-dimensional discrete torus
We prove that a uniformly chosen proper coloring of Z2nd with 3 colors has a very rigid structure when the dimension d is sufficiently high. The coloring almost surely takes one color on almost all of either the even or the odd sub-lattice. In particular, one color appears on nearly half of the lattice sites. This model is the zero temperature case of the 3-states anti-ferromagnetic Potts model, which has been studied extensively in statistical mechanics. The proof involves results about graph homomorphisms and various combinatorial methods, and follows a topological intuition. Joint work with Ron Peled.