Shape, Homology, Persistence, and StabilityHerbert Edelsbrunner
Institute of Science and Technology, Austria
Abstract: My personal journey to the fascinating world of geometric forms started more than 30 years ago with the invention of alpha shapes in the plane. It took about 10 years before we generalized the concept to higher dimensions, we produced working software with a graphics interface for the 3-dimensional case. At the same time, we added homology to the computations. Needless to say that this foreshadowed the inception of persistent homology, because it suggested the study of filtrations to capture the scale of a shape or data set. Importantly, this method has fast algorithms. The arguably most useful result on persistent homology is the stability of its diagrams under perturbations.
Bio sketch: Herbert Edelsbrunner is a professor of mathematics and computer science at IST Austria and a co-founder of Geomagic. He works in the field of computational geometry and topology as well as its applications in science and engineering. He is the author or co-author of four textbooks in the wider area.
Emerging Topics in Network VisualizationKwan-Liu Ma
University of California at Davis, USA
Abstract: Visualizing networks commonly found in a wide variety of applications, such as bioinformatics, computer security, social networks, telecommunication, transportation systems, etc., can lead to important insights. While visualizing small, static networks is relatively easy to do, larger and more complex networks present many challenges. In particular, real-world network data are almost all time-varying, and effective techniques for visualizing and analyzing networks evolving over time are lacking. I will discuss emerging topics in network visualization using research results that my group has produced as examples.
Bio sketch: Kwan-Liu Ma is a professor of computer science and the chair of the Graduate Group in Computer Science (GGCS) at the University of California at Davis, where he leads the Visualization and Interface Design Innovation (VIDI) research group and directs the UC Davis Center for Visualization. His research spans the fields of visualization, computer graphics, high-performance computing, and user interface design.