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,…
The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed netflow at each vertex. We will examine flow polytopes arising from permutation matrices, alternating sign matrices and Tesler matrices. Our inspiration is the Chan-Robins-Yuen polytope (a face of the polytope of…
In general, solutions to the Laplacian equation enjoy relatively high smoothness. However, they can exhibit singular behaviors at domain corners or points where boundary conditions change type. In this talk, I will focus on the mixed Dirichlet-Neumann boundary conditions for Laplacian equation, and discuss how singularities in this case adversely affect the accuracy and convergence…
In joint work with Rafal Komendarczyk and Ismar Volic, we study the space of braids, that is, the loopspace of the configuration space of points in a Euclidean space. We relate two different integration-based approaches to its cohomology, both encoded by complexes of graphs. On the one hand, we can restrict configuration space integrals for…
One of the primary goals of text mining is to group together, organize and summarize textual information. In social network analysis, we typically tie individuals together through social connections — can we connect documents and their contents in a similar fashion? What can social network analysis tell us about the content of a document or…
The evolution, through spatially periodic linear dispersion, of rough initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. Such phenomena, also known as the Talbot effect, have been observed in dispersive waves, optics, and quantum mechanics, and lead to intriguing connections with exponential sums arising in number…
In this talk we discuss an algorithm to overcome the curse of dimensionality, in possibly non-convex/time/state-dependent Hamilton-Jacobi partial differential equations. They may arise from optimal control and differential game problems, and are generally difficult to solve numerically in high dimensions. A major contribution of our works is to consider an optimization problem over a single…