Abstract: Advances in simulation and scientific machine learning have made computation an engine of discovery. For increasingly complex physical systems, however, computational scale and model expressiveness alone may not suffice for faithful simulation, exploration, and inverse design. General-purpose representations often describe a space much larger than the set of physically admissible states. Computing in this larger space can require substantial effort to ensure that solutions respect the underlying geometry, topology, and conservation laws. A complementary path is to make this structure explicit. Through examples ranging from bending rods and slithering snakes to fluid flows and magnetic fields in plasmas, this talk shows how geometric insight can make difficult problems computationally tractable, how the resulting structure can be preserved and encoded in algorithms, and how the exchange among theory, discretization, and application yields new mathematics alongside more effective computational tools.
Bio: Oliver Gross is a postdoctoral researcher at the University of California San Diego, working with Prof. Albert Chern. His research lies at the interface of applied mathematics, computer graphics, and physics simulation. He uses the geometric structures underlying natural phenomena to develop accurate and efficient methods for simulation, optimization, and inverse design, with applications to fluids and plasmas, elastic and soft bodies, locomotion, and robotics. He received his Ph.D. in Mathematics, summa cum laude, from TU Berlin under Prof. Ulrich Pinkall and Prof. Peter Schröder and was previously a postdoctoral researcher with Prof. Mark Pauly at EPFL.
Abstract: Advances in simulation and scientific machine learning have made computation an engine of discovery. For increasingly complex physical systems, however, computational scale and model expressiveness alone may not suffice for faithful simulation, exploration, and inverse design. General-purpose representations often describe a space much larger than the set of physically admissible states. Computing in this larger space can require substantial effort to ensure that solutions respect the underlying geometry, topology, and conservation laws. A complementary path is to make this structure explicit. Through examples ranging from bending rods and slithering snakes to fluid flows and magnetic fields in plasmas, this talk shows how geometric insight can make difficult problems computationally tractable, how the resulting structure can be preserved and encoded in algorithms, and how the exchange among theory, discretization, and application yields new mathematics alongside more effective computational tools.
Bio: Oliver Gross is a postdoctoral researcher at the University of California San Diego, working with Prof. Albert Chern. His research lies at the interface of applied mathematics, computer graphics, and physics simulation. He uses the geometric structures underlying natural phenomena to develop accurate and efficient methods for simulation, optimization, and inverse design, with applications to fluids and plasmas, elastic and soft bodies, locomotion, and robotics. He received his Ph.D. in Mathematics, summa cum laude, from TU Berlin under Prof. Ulrich Pinkall and Prof. Peter Schröder and was previously a postdoctoral researcher with Prof. Mark Pauly at EPFL.