腾讯会议ID：418 227 590

会议链接：https://meeting.tencent.com/s/4M7QFoY5DCgN

There is a close relation between Maxwell’s equations and the de Rham complex. The perspective of continuous and discrete differential forms has inspired key progress in computational electromagnetism. This complex point of view also plays an important role in, e.g., continuum theory of defects, intrinsic elasticity and relativity.

In this talk, we briefly review the de Rham complexes and their smoother versions, known as the Stokes complexes with applications in fluid mechanics. Then we generate new complexes from them and study their algebraic and analytic properties. As an example, we construct Sobolev and finite element elasticity complexes by diagram chasing. Special cases of this cohomological approach generalize results in classical elasticity, e.g., the Korn inequality and the Cesàro-Volterra path integral.