Speaker: Derek Frydel (Universidad Técnica Federico Santa María)Title: Hidden Dualities in Nonequilibrium Transport: How Stationary States Encode First-Passage ProcessesAbstract: First-passage processes and stationary states are traditionally regarded as distinct aspects of stochastic dynamics, governed by the backward and forward evolution equations, respectively. In this seminar, I will discuss how the backward equation can be reinterpreted as the forward equation of a dual stochastic process. This observation introduces a dual stochastic system whose stationary observables can be directly related to first-passage quantities of the original physical system. I will first discuss the application of this duality formalism to active matter under wall confinement. Using the duality relation, I will show how the tendency of active particles to become dynamically adsorbed at confining walls directly encodes certain features of splitting probabilities, revealing stationary accumulation and first-passage behavior as complementary manifestations of directional persistence. In the second part of the talk, I will shift from boundary confinement to bulk transport by applying the same duality formalism to effective diffusion in periodic force fields. Since the effective diffusion coefficient is fundamentally related to first-passage-time moments, it provides a natural setting in which stochastic duality can be applied. I will discuss how the effective diffusion coefficient can be formulated entirely in terms of stationary distributions of the physical and dual systems, providing a new perspective on transport in periodically driven nonequilibrium systems. Bio: Derek Frydel is an Associate Professor at the Universidad Técnica Federico Santa María. Professor Frydel’s research interest is in theoretical research of soft-matter systems. Frydel uses a broad range of computational and analytical methods, and his research overlaps with physics, chemistry, biology, mathematics, and industry The NSF-Simons National Institute for Theory and Mathematics in Biology Seminar Series brings together a mix of mathematicians and biologists to foster discussion and collaboration between the two fields. The seminar series typically takes place on Fridays from 10am – 11am at NITMB. Talks are in-person with the ability to join remotely. More information – https://www.nitmb.org/nitmb-seminar-series (https://www.nitmb.org/nitmb-seminar-series)