Persistent homology is a key method in topological data analysis, a young but rapidly growing field at the intersection of computational geometry and algebraic topology. Persistence is used to describe the shape of data in a way that generalizes clustering: besides considering what connected components (clusters) are present in the data, it also describes their…
Many estimates in analysis have certain “common structures” which makes it possible to obtain them with what is now called Bellman function method. Originally the method appeared in control theory (stochastic or deterministic), however its systematic use in harmonic analysis or probability started only recently in works of Burkholder where he obtained the sharp constants…
The mitotic spindle is a complex, dynamic machine important for cell division. The spindle is composed of a network of microtubules and motor proteins that generate forces to form a bipolar spindle, with each pole organized around a single centrosome. Disruption in force generating activities through protein depletions or alterations to centrosome number, alter spindle…
Homology 3-spheres, i.e. 3-dimensional manifolds with the same homology groups as the standard 3- sphere, play a central role in topology. Their study was initiated by Poincare in 1904, who constructed the first nontrivial example of a homology 3-sphere, and conjectured that the standard sphere is the only simply connected example. A century later, Poincare's…
The AWM Chapter is organizing a Math Research Competition on Saturday, February 29, here at NCSU (the poster is attached). The program includes 2 keynote lectures, two parallel sessions of lightning talks (one in math, and one in applied math), and a poster session. Awards will be given to top presentations and posters. Lunch is provided for all participants. Therefore,…
Chairs: Ernie Stitzinger, Scott Batson
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space (E, ρ) up to an accuracy of epsilon > 0 with respect to the L^1-distance. Such an estimate is explicitly computed in terms of…
Chair: Kevin Flores
This event has been rescheduled for August 25. We present a fast and accurate numerical method for the simulation of time domain scattering problem. Both acoustic and electromagnetic scattering problems are discussed. Nonreflecting boundary conditions (NRBCs) are used to truncate the problem. We first derive analytic expressions for the underlying convolution kernels which allow for a rapid and accurate…