Almost invariant differential calculus -- Jan Slovak (Masaryk University), PHK 17.05.2023

Title: Almost invariant differential calculus
Speaker: Jan Slovak (Masaryk University)

Abstract:
For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general tools were presented for the entire class of parabolic geometries, i.e., the Cartan geometries modelled on homogeneous spaces G/P with P a parabolic subgroup in a semi-simple Lie group G. Similarly to conformal Riemannian and projective structures, all these geometries determine a class of distinguished affine connections, which carry an affine structure modelled on differential 1-forms . They correspond to reductions of P to its reductive Levi factor, and they are called the Weyl structures similarly to the conformal case. The standard definition of differential invariants in this setting is as affine invariants of these connections, which do not depend on the choice within the class. In this talk, we describe a universal calculus which provides an important first step to determine such invariants. I shall present a natural procedure how to construct all affine invariants of Weyl connections, which depend only tensorially on the deformations. This is a joint work with Andreas Cap.


Talk given at the Prague-Hradec Králové seminar on Cohomology in algebra, geometry, physics and statistics:

https://calendar.math.cas.cz/content/...
https://researchseminars.org/talk/PHK...