Chris from DELTA will be leading an interactive seminar on what Moodle is, a jump start, and answering any questions you have for the platform and it's capabilities. You'll have the opportunity to go hands on with them as they walk you through the platform. Regardless of your experience with Moodle, I encourage you to…
Semidefinite programs (SDPs) -- optimization problems with linear constraints, linear objective, and semidefinite matrix variables -- are some of the most useful, versatile, and pervasive optimization problems to emerge in the last 30 years. They find applications in combinatorial optimization, machine learning, and statistics, to name just a few areas. Unfortunately, SDPs often behave pathologically: the optimal values of the primal…
We consider an approximating control design for optimal mixing of a non-dissipative scalar eld in unsteady Stokes ows. The objective of our approach is to achieve optimal mixing at a given nal time, via an active control of the ow velocity through boundary inputs. Due to the zero diusivity of the scalar eld, establishing the well-posedness of its…
In full-tensor extensions of 1D interpolation or quadrature rules, the number of nodes will grow exponentially in the dimension—commonly called the “curse of dimensionality.” In this talk, we present an overview of sparse grids, in which the number of nodes grows only polynomially in the dimension. First, we will do an overview of 1D interpolation for…
We prove results about the polytope associated to the toric ideal of invariants of the Cavender-Farris-Neyman model with a molecular clock on a rooted phylogenetic tree. For instance, the number of vertices of this polytope is a Fibonacci number and the facets of the polytope can be described using the combinatorial structure of the underlying…
In many applications one wishes to minimize an objective function that is not convex and is not differentiable at its minimizers. We discuss two algorithms for minimization of nonsmooth, nonconvex functions. Gradient Sampling is a simple method that, although computationally intensive, has a nice convergence theory. The method is robust and the convergence theory has…
Radmila Sazdanović will speak at the Coffee and Viz series in the Teaching and Visualization Lab, James B. Hunt Jr. Library on Friday March 16, 9:30-10:30 am about Visual Mathematics: the role of visualizations in math research.
In many applications one wishes to minimize an objective function that is not convex and is not differentiable at its minimizers. We discuss two algorithms for minimization of nonsmooth, nonconvex functions. Gradient Sampling is a simple method that, although computationally intensive, has a nice convergence theory. The method is robust and the convergence theory has…
We will describe an adaptation of the theory of trisections to the setting of properly embedded, smooth, compact surfaces in smooth, compact, orientable four-manifolds with boundary. The main result is that any such surface can be isotoped to lie in bridge trisected position with respect to a given trisection on the ambient four-manifold. The trisection…
The lecture will consider the case of evolution equations, endowed with a "free energy," for which the initial value problem possesses multiple solutions, with an eye to examining whether the particular solution that maximizes the rate of energy decay enjoys a special status.
Effective webpages are an increasingly important medium for disseminating information related to classes and research. For TAs, they provide a critical way to share material with your class whereas for those entering the job market, they are often checked by potential employers interested in obtaining more information about candidates. Hence it is important to construct…
The Triangle Lectures in Combinatorics is a series of combinatorial workshops held each semester on a Saturday in the Research Triangle region of North Carolina, funded by the National Science Foundation. The workshop this spring, the 15th installment of the Triangle Lectures in Combinatorics (TLC), will be hosted by North Carolina State University in Raleigh,…