Institute of Mathematics

Talk

Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

Complexes from complexes

Dr. Kaibo Hu talk

Date: 14.10.20  Time: 16.15 - 17.45  Room: Online ZHACM

There is a close connection between the Maxwell equations and the de Rham complex. The perspective of continuous and discrete differential forms has inspired key progress in the mathematical and numerical analysis for electromagnetism. This complex point of view also plays an important role in, e.g., continuum theory of defects, intrinsic theories of elasticity and relativity. In this talk, we derive new differential complexes from the de Rham complexes. The algebraic construction is inspired by the Bernstein-​Gelfand-Gelfand (BGG) machinery. The cohomological structures imply various analytic properties. As an example, we construct Sobolev and finite element elasticity complexes (Kröner complex in mechanics and the linearized Calabi complex in geometry) and generalize various results in classical elasticity, e.g., the Korn inequality and the Cesàro-​Volterra path integral.