##### Department of Mathematics,

University of California San Diego

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### Extra Analysis Seminar

## Prof. Jan Slovak

#### Masaryk U

## Nearly invariant calculus for a few CR (and all parabolic) geometries

##### 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, projective geometries, hypersurface type CR geometries, etc.. More recently, general tools were presented for the entire class of the so called 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. 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 we call them 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 the lecture, I shall describe a universal calculus which provides an important first step to determine such invariants. The lecture will follow the recent preprint https://arxiv.org/

### November 17, 2022

### 3:00 PM

APM 7218

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