프로그램
서인석
Title: Interacting Brownian motions with local interaction
Abstract: In this lecture, we review the hydrodynamic limit theory for a system of interacting Brownian motions with local type interaction. More precisely, we will derive the hydrodynamic limit of two-color system and multicolor system which are non-gradient models and hence usual replacement technique does not work. Based on this result, we also derive the large deviation principle for the two-color system. Moreover, we can derive the limiting theory and large deviation principle for the tagged particle or empirical processes based on the limiting procedure such as Dawson-Gartner theory. We shall also discuss future research direction toward the interacting Brownian motions with double-well interaction.
남경식
Title: Universality for Spectral Large Deviations of Sparse Random Matrices
Abstract: Universality for the eigenvalues of random matrices has been intensively studied in the random matrix community for a long time. A natural generalized version of Wigner matrices is called sparse or diluted random matrices, where each entry is multiplied by the independent Bernoulli random variable with mean p. When the sparsity is given by p = 1/n, the most interesting regime due to its connection with statistical mechanics, universality breaks down and the eigenvalue statistics has not been understood yet. In this talk, I will talk about the universality and a precise spectral behavior of such sparse random matrices. Joint work with Shirshendu Ganguly and Ella Hiesmayr.
유화종
Title: Riemann zeta function and Riemann hypothesis
Abstract: In this series of lectures, we introduce the Riemann zeta function and Riemann hypothesis. We first define the Riemann zeta function on Re(s)>1. Using the Gamma function, we show that the "complete zeta function" satisfies functional equation. If time permits, we dicuss relations between the statistical behaviour of the nontrivial zeros of the Riemann zeta function and that of the eigenvalues of large random matrices.
유명준
Title: A Markov process for the distribution of 2-Selmer ranks of Jacobians of hyperelliptic curves in the family of quadratic twists
Abstract: Klagsbrun, Mazur and Rubin used Markov chain to study the distribution of 2-Selmer ranks of elliptic curves in the family of quadratic twists. They proved that the probability that the 2-Selmer rank of an elliptic curve is equal to a non-negative integer r is given by some constant, which is defined combinatorially. We show that there is the same distribution for 2-Selmer ranks of Jacobians of hyperelliptic curves assuming a heuristic hypothesis.