Aaron Yip, Purdue University
Abstract: Despite a long history and many results on motion by mean curvature and homogenization, there are still many interesting questions when these two problems are put together. This is a typical question of gradient flow on wiggly energy landscapes. The talk will revisit the problem of motion by…
Eitan Tadmor, University of Maryland
A fascinating aspect of collective dynamics is self-organization of small scale interactions into high-order structures with larger-scale patterns. It is a characteristic feature of “social particles” which actively probe the environment and emerge in various types of clusters. In different…
Kelsey Gasior, University of Ottawa, Canada
An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquidlike droplets condense to create compartments that are thought to localize factors, such as RNAs and proteins, and promote biochemical…
Shuang Liu, UC San Diego
Moving boundary (or often called “free boundary”) problems are ubiquitous in nature and technology. A computational perspective of moving boundary problems can provide insight into the “invisible” properties of complex dynamics systems, advance the design of novel technologies, and improve the…
Gregory Handy, University of Chicago
Stochastic fluctuations drive biological processes from particle diffusion to neuronal spike times. The goal of this talk is to use and extend a variety of mathematical frameworks to understand such fluctuations and derive insight into the corresponding applications. We start by considering n…
Julian Chaidez, Princeton University
Symplectic dynamics is the study of dynamical systems using tools from symplectic topology, like Floer homology. Many natural dynamical systems in physics and topology can be studied fruitfully through this lens, including many-body problems, billiards and surface diffeomorphisms.
In this…
Maziar Raissi, University of Colorado Boulder
Abstract: A grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviours expressed by differential equations with the vast data sets available in many fields of engineering…
Peijie Zhou, UC Irvine
Abstract: The rapid development of single-cell sequencing technologies provides unprecedented resolutions to study the dynamical process of cell-state transitions during development and complex disease. Mathematically, the transitions can be modeled as a (stochastic) dynamical system with a multi-scale…
Filippo Mazzoli, University of Virginia
Abstract: The focus of this talk will be the study of representations of the fundamental group of a closed orientable surface of genus g (in short, a surface group) inside the Lie groups PSL(n,C), for any g and n larger than 1. Surface group representations inside PSL(2,C) (such as quasi-…
Hana Jia Kong, Institute for Advanced Study
Abstract: For the past 90 years, a fundamental question in classical homotopy theory is to understand the stable homotopy groups of spheres. The most modern method to study these groups is to compare them with the ``motivic stable homotopy groups of spheres". Motivic homotopy theory…