1.
Time: May 22nd (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Jaeyoung Yoon (Seoul National University)

Title: Measure-valued death state and local sensitivity analysis for Winfree model with uncertain high-order couplings

Abstract:
We study the measure-valued death state and local sensitivity analysis of the Winfree model and its mean-field counterpart with uncertain high-order couplings. The Winfree model is the first mathematical model for synchronization, and it can be cast as the effective approximation of the pulse-coupled model for synchronization, and it exhibits diverse asymptotic patterns depending on system parameters and initial data. For the proposed models, we present several frameworks leading to oscillator death in terms of system parameters and initial data, and the propagation of regularity in random space.

2.
Time: May 29th (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Seonwoo Kim (Korea Institute for Advanced Study)

Title: Hierarchical metastability structure in the reversible inclusion process

Abstract:
In this talk, I will discuss the hierarchical decomposition of metastability, which is ubiquitous in stochastic dynamical systems with complicated energy landscapes, and in particular the mechanism that triggers such a multi-scale phenomenon. Then, to fix ideas, I will focus on a specific example, the reversible inclusion process on a finite graph, where the hierarchical structure is based on the graph distance between the sites with maximum invariant measure. Then, I will briefly sketch the idea of proofs for the main theorems.