I will discuss some theoretical and numerical results on the stability properties of a dynamical system modeled by a nonlinear wave equation with a "degenerate" damping. The coefficient of the dissipation term is proportional to the amplitudes, hence its support depends on the geometry of the solution. This feature substantially complicates the stability analysis even…
You've probably heard some old guy rant about Newton's method and how it will solve all of your problems: linear, nonlinear, personal, laundry. There's more. In this talk I'll tell you about a way to accelerate plain vanilla fixed point iteration. The first theory for this stuff came from right here in SAS hall and…
The Schur-Weyl duality between the symmetric group and the general linear group allows us to connect the representation theory of these two groups. A consequence of this duality is the Frobenius formula which connects the irreducible characters of the general linear group and the symmetric group via symmetric functions. The symmetric group is also in…
This talk will introduce a primal-dual finite element method for variational problems where the trial and test spaces are different. The essential idea behind the primal-dual method is to formulate the original problem as a constrained minimization problem. The corresponding Euler-Lagrange formulation then involves the primal (original) equation and its dual with homogeneous data. The…
Please join us for our weekly brown bag lunch! You bring your lunch, and we will bring a delicious treat. Everyone (not just women) is welcome to join or stop by for as long as they can!
Many important Lie (super)algebras can be constructed using bosonic and fermionic oscillators. We introduce inhomogeneous supersymmetric bilinear forms on a complex superspace and show that they lead to oscillator-like superalgebras. We classify such forms for superspaces up to dimension 7 and mention a few examples of subalgebras obtained from the corresponding superalgebras. This talk is…
I will explain some interesting selection problems in nonlinear PDEs. The basic question is about how to select one good solution out of many reasonable ones. A question of this type led to the whole theory of viscosity solutions in 1980s. Then I will focus on the vanishing discount problem and describe the main results,…
Control theory is an important topic in applied mathematics that is used in a number of disciplines. Its theoretical foundations involve several areas of mathematics. It is also a topic that is less well known at the undergraduate level. In this talk we will explain what control theory is and give several elementary examples of specific kinds of…
Advised by Nathan Reading.
Advised by Lorena Bociu.
Mixtures of Gaussians are ubiquitous in data science. We give an introduction to the geometry of these statistical models, with focus on the tensors that represent their higher moments. The familiar theory of rank and borderrank for symmetric tensors is recovered when all covariance matrices are zero. Recent work with Carlos Amendola and Kristian Ranestad…
Please join us for our weekly brown bag lunch! You bring your lunch, and we will bring a delicious treat. Everyone (not just women) is welcome to join or stop by for as long as they can!