Abstract:
In the early 80’s, Giorgio Parisi wrote a series of ground breaking papers where he introduced the notion of replica symmetry breaking. His powerful insight allowed him to predict a solution for the SK model by breaking the symmetry of replicas infinitely many times. In this talk, we will prove Parisi's prediction at zero temperature for the mixed p-spin model, a generalization of the SK model. We will show that at zero temperature the functional order parameter is full-step replica symmetry breaking (FRSB). We will also describe the importance of this result for the description of the energy landscape. Based on works with Wei-Kuo Chen (University of Minnesota) and Qiang Zeng (Northwestern University).
Biography:
Antonio Auffinger is Associate Professor at Northwestern University. He obtained his Ph.D. in mathematics at the New York University in 2011. Before joining Northwestern, Auffinger was a L.E. Dickson Instructor at the University of Chicago. He works in probability theory and his research interests include complex disordered systems such as spin glasses, first-passage percolation, and random matrix theory. His research is currently supported by an NSF CAREER award, the most prestigious award in support of early-career faculty in the USA.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai