Affine Lie algebras, also sometimes called current algebras, are infinite-dimensional analogs of finite-dimensional semisimple Lie algebras. The representation theory of affine Lie algebras has applications in many areas of mathematics…
We review randomized algorithms for the numerical solution of least squares/regression problems, with a focus on algorithms that row-sketch from the left, or column-sketch from the right. These algorithms tend…
Beginning with the solution of the classical Plateau problem—the problem of finding an area-minimizing disk whose boundary is a prescribed simple closed curve in Euclidean 3-space—we will survey some applications…
When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics.…
I and many collaborators, postdocs, and students from many disciplines have explored lung mechanics and disease pathology for over 2 decades in a pan-university effort called the UNC Virtual Lung…
In this talk we will discuss the connection between invariant evolutions of polygons and completely integrable discrete systems via polygonal geometric invariants. We will give examples and show how some…
Synthetic aperture radars (SAR) use microwaves to obtain images of the Earth's surface from airplanes or satellites. SAR images can be taken during nighttime and prove insensitive to the clouds…
The vision of Isogeometric Analysis (IGA) was first presented in a paper published October 1, 2005 . Since then it has become a focus of research within both the fields…
I will begin by probing into the past to discover the origins of the Finite Element Method (FEM), and then trace the evolution of those early developments to the present…
In linear algebra we know that the Pfaffian of an antisymmetric matrix is a square root of the determinant of matrix. In this talk I will explain how one does…
Congenital heart disease affects 1 in 100 infants and is the leading cause of infant mortality in the US. Among the most severe forms of congenital heart disease is single…
We introduce a Swarm-Based Random Descent (SBRD) method for non-convex optimization. The swarm consists of agents, identified with positions, x, and masses, m. There are three key aspects to the…
Simulating the time evolution of a Hamiltonian system on a classical computer is hard—the computational power required to even describe a quantum system scales exponentially with the number of its…
The climate is changing due to the heat trapping caused by the rapid increase in greenhouse gases, mainly carbon dioxide, in the atmosphere. One way to state the issue is…
Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to…
Minimal surfaces are fundamental geometric objects which have been studied intensively since the 1700's. Classes of minimal surfaces of particular interest are the complete embedded ones in Euclidean space, closed…