This website is created in support of a Multi-University Research Initiative (MURI) sponsored by the Air Force, under award number FA9550-20-1-0397, to analyze, understand, and synthesize rare but consequential events.
Earthquakes, tsunamis, volcanic eruptions; pandemics, stock market crashes, currency crises---all these are events that seldom occur within the ordinary spatial and/or temporal scales of a system, and yet have an enormous impact when they do occur. In Air Force applications, rare events of interest include aircraft engine failures, fatigue, and fracture in aero-structural components, lightning or bird strikes on aerospace vehicles, and countless more. The impact of these events lends practical urgency to the development of a comprehensive mathematical theory for the modeling, prediction, and prevention of rare events.
Our goal is to develop a comprehensive framework that can be used to systematically study rare events in a wide range of settings, and we will develop the mathematical and computational tools necessary to apply our framework. While these developments are intended to be foundational and general, they are grounded in---and will be applied to---realistic applications in materials science, environmental engineering, mean-field phenomena, and networks.
Research Interest: Applied probability, Computational finance, MCMC, Queueing theory, Rare-event analysis, Simulation methodology, and Risk theory.
Personal WebsiteResearch Interest: Predicting mechanical strength of materials through theory and simulations of defect microstructures across atomic, mesoscopic and continuum scales. Developing new atomistic simulation methods for long time-scale processes, such as crystal growth and self-assembly. Introducing magnetic field in quantum simulations of electronic structure and transport.
Personal WebsiteResearch Interest: Numerical methods for solving mathematical problems arising in natural sciences including geophysics, chemical physics, and biology, spliting between Hamilton-Jacobi solvers for nonlinear PDEs and greedy graph algorithms for analysis of complex networks.
Personal WebsiteResearch Interest: Intersection of computation and statistical inference with physical modeling, including new methodologies for uncertainty quantification, Bayesian modeling and computation, data assimilation, experimental design, and machine learning in complex physical systems.
Personal WebsiteResearch Interest: Theory and modeling of nanoscale materials for electronics and energy applications, and materials at conditions of extreme temperatures, pressures, and fields. His work to date has focused on 2D materials, high pressure shock wave compression, THz radiation generation, phase change materials, materials informatics approaches, energetic materials, and photonic crystals.
Personal WebsiteResearch Interest: Mechanical behavior of materials and structures. Basic processes include fracture, deformation, polarization, and diffusion, driven by various thermodynamic forces (e.g., stress, electric field, electron wind, chemical potential). Applications are concerned with microelectronics, large-area electronics, soft materials, active materials, and lithium-ion batteries.
Personal WebsiteResearch Interest: Representation, modeling, inference and prediction from data such as determining how different people will respond to exposure to certain viruses, predicting rare events from small amounts of data, formulation and calculation of limits of learning from observations, and prediction of a macaque monkey's future actions from its brain waves.
Personal Website