While the fields of geometric design and numerical simulation have mostly evolved independently, we are now witnessing a convergence of thought: from isogeometric analysis, to geometric integrators and discrete exterior calculus, it has been repeatedly noted that the quality of computational tools ultimately boil down to properties of a fundamentally geometric or topological nature. This talk will describe a brief overview of our approach to computing through the lens of geometry to offer a versatile and efficient toolbox for a variety of applications, from shape processing to tangent vector field editing, and from fluid simulation to non-linear dimensionality reduction. We will point out how a strong grasp of classical differential geometry paired with a good understanding of the typical computational constraints in research and industry can bring forth novel theoretical and practical foundations for general-purpose computations. The importance of preserving differential geometric notions in the discrete setting will be a recurring theme throughout the talk to demonstrate the value of a geometric approach to computations.
Bio: After obtaining a PhD in computer graphics in Grenoble, Mathieu Desbrun joined Caltech as a postdoctoral fellow in 1998. He joined the CS department at the University of Southern California as an Assistant Professor in January 2000, where he remained for four years in charge of the GRAIL lab. He then became an Associate Professor at Caltech in the CS department in 2003, where he started the Applied Geometry lab and was awarded the ACM SIGGRAPH New Researcher award. He took on administrative duties after he became a full professor, becoming the founding chair of the Computing + Mathematical Sciences department and the director of the Information Science and Technology initiative from 2009 to 2015. More recently, he received an International Chair from France’s Inria, has been the Technical Papers Chair for the ACM SIGGRAPH 2018 conference, and has just completed a sabbatical year at ShanghaiTech.