Toronto, December 2 - 5, 2022
In this talk, I will begin by presenting an overview of the field and my various contributions to it, with emphasis on visibility and pursuit-evasion problems These topics have significant research and industry interest due to their numerous applications, including wireless communications, robotics, computer graphics, and surveillance. Following this, I will discuss the interdisciplinary works which arise from close collaborations with engineering and machine learning groups, such as medical imaging, additive manufacturing, geometric deep learning.
The importance of the link between theory and application cannot be understated, as it is through the study of the theory that we can improve and expand the reach of applications; it is also through the present challenges faced in applications by which theoretical research can be informed. My ultimate goal is to extend the reach and relevance of Computational Geometry, and further its integration in new domains.
The talk is based on joint work with D.Kinzebulatov and Yu.A. Semënov.
Based on work with Beomjun Choi (Postech) and Christian Seis (Muenster)
In this talk we will look at some reductions of general fluid dynamics equations, including popular and less well known shallow water PDE models. Such models arise in a wide variety of settings within and beyond fluid surface waves. We will discuss some important analytical properties of such models with emphasis on those that are systematically computable. Examples of computation and applications of elements of analytical structure will be given for several PDE systems.
Recently, Schneider initiated the study of the Minkowski type problems for $C$-close sets, a family of (unbounded) closed convex sets contained in a cone. In this talk, I will talk about our recent progress on the Minkowski type problems for unbounded convex hypersurfaces. These Minkowski type problems generate new Monge-Ampere type equations. The solutions to these Minkowski type problems will also be presented.