Arvind Ayyer completed his PhD at Rutgers University, USA, in physics in 2008, which was followed by a postdoctoral fellowship at CEA Saclay in France until 2010. He then joined the University of California at Davis as Krener Assistant Professor in the mathematics department. After short-term visiting positions at MSRI and TIFR, Ayyer joined IISc as Assistant Professor in 2013. He was selected as an Associate of the Indian Academy of Sciences in 2014.
Session 1C: Inaugural Lectures by Fellows/Associates
Exactly solvable models of nonequilibrium statistical physics play a key role in developing intuition about what kind of behaviour one can expect in such systems. The asymmetric simple exclusion process (ASEP) is an exactly solvable model for nonequilibrium physics that models particle transport. In importance, it plays a role similar to the Ising model in equilibrium physics. The ASEP and some exact nonequilibrium computations will be introduced.
The ASEP can be naturally generalized to a model with several species of particles. The work of the speaker’s groups to compute the exact stationary distribution of the multispecies ASEP will be presented. How a conjecture by T. Lam on the limiting direction of a random walk in an affine Weyl group was solved somewhat unexpectedly by computing correlation functions in the multispecies ASEP, will be demonstrated. Recent results on the exact phase diagram of a multispecies ASEP with open boundaries will be discussed.