Events
Ryan Murray, Pennsylvania State University, An introduction to singular perturbations in the calculus of variations
SAS 4201Many contemporary problems in the calculus of variations involve describing the limit of singular perturbations of variational problems. These problems arise naturally in a number of fields, for example in materials science (phase transition problems) and mathematical statistics (regularized empirical risk minimization). This talk will give an introduction to these problems, their applications, and recent work…
Departmental Tea and Cookies
SAS 4104Mohammad Farazmand, MIT, Extreme Events: Dynamics, Prediction and Mitigation
SAS 4201A wide range of natural and engineering systems exhibit extreme events; i.e., spontaneous intermittent behavior manifested through sporadic bursts in the time series of their observables. Examples include ocean rogue waves, intermittency in turbulence, extreme weather patterns and epileptic seizure. Because of their undesirable impact on the system or the surrounding environment, the real-time prediction and mitigation of extreme events is of great interest.…
Yakov Berchenko-Kogan, Washington University in St. Louis, Variational numerical methods in geometric PDE
Variational methods can be used to create numerical methods that respect conservation laws. I will discuss applications to electromagnetism, the Yang-Mills equations, and mean curvature flow. I will also discuss some new ideas about finite element spaces of differential forms.
Departmental Tea and Cookies
SAS 4104Anne Shiu, Texas A&M, Dynamics of biochemical reaction systems
SAS 4201Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. This talk focuses on certain biological signaling networks, namely, phosphorylation networks, and their resulting dynamical systems. For many of these systems, the set of steady states admits a rational parametrization (that is, the set is the image of a map…
Departmental Tea and Cookies
SAS 4104Mark Iwen, Michigan State University, Sparse Fourier Transforms, Generalizations, and Extensions
SAS 4201Compressive sensing has generated tremendous amounts of interest since first being proposed by Emmanuel Candes, David Donoho, Terry Tao, and others roughly a decade ago. This mathematical framework has its origins in (i) the observation that traditional signal processing applications, such as MRI imaging problems, often deal with the acquisition of signals which are known…
Departmental Tea and Cookies
SAS 4104Pierre-Emmanuel Jabin, University of Maryland, Critical scales for the regularity of advection equations and applications to compressible fluid mechanics
This talk will present recent works to identify the critical scales at which regularity is propagated by advection equations with rough, i.e. non-smooth, velocity fields. After reviewing the classical theory of renormalized solutions which provides qualitative arguments of regularity and well-posedness, more recent quantitative approaches will be discussed. Our goal is to use this framework…
Weekly Brown Bag Lunch
SAS 4104Join us tomorrow Wednesday 1/16/19 from 12:00-1:00 in the math graduate lounge for our first weekly brown bag lunch of the semester. As a reminder all are welcomed including undergraduate students! There will be goodies!
Departmental Tea and Cookies
SAS 4104Khrystyna Serhiyenko, University of California at Berkeley, Cluster structures in Grassmannian and Schubert varieties
SAS 4201Cluster algebras are commutative rings defined by a set of generators and relations and equipped with a rich combinatorial structure. It turns out that coordinate rings of many important varieties from Lie theory are cluster algebras. In this talk, we will discuss cluster structures in open Schubert varieties of the Grassmannian and their…
Departmental Tea and Cookies
SAS 4104Alpar Meszaros, UCLA, Mean Field Games and Master Equations
SAS 4201The theory of Mean Field Games was invented roughly a decade ago simultaneously by Lasry-Lions on the one hand and Caines-Huang-Malhamé on the other hand. The aim of both groups was to study Nash equilibria of differential games with infinitely many players. In the first half of the talk, we will introduce some basic models…