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16.01.2025, 16:30+  –  Raum 0.14
Forschungsseminar Differentialgeometrie

The Rarita-Schwinger Operator on the 3-Sphere with Homogeneous Metric

Peter Grabs

We investigate the Rarita-Schwinger operator using methods previously applied in the Dirac case. The structure of the underlying manifold as a Lie group implies... 

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12.12.2024, 16:15  –  Raum 0.14
Forschungsseminar Differentialgeometrie

First steps towards an equivariant Lorentzian index theorem

Lennart Ronge (UP)

This is a work-in-progress description on an unfinished approach to proving a Lorentzian version of the equivariant index theorem, which assigns an index to a Dirac operator in the presence of a group... 

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05.12.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

The equivariant index theorem with boundary.

Lennart Ronge

Given a Dirac type operator on a manifold with boundary and a group action that preserves all relevant structures, one can define a generalized index for any group element. Analogous to the APS index... 

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07.11.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Scalar curvature along Ebin geodesics

Christoph Böhm (Münster)

Let be a smooth, compact manifold and let  denote the set of Riemannian metrics on with a fixed smooth volume density of volume 1. For any  , we show that... 

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24.10.2024, 16:15  –  2.09.0.14
Forschungsseminar Differentialgeometrie

Dominant energy condition and invertibility of the Dirac-Witten operator

Bernd Ammann (Regensburg)

The classical Atiyah-Singer theorem tells us: if is a closed spin manifold, carrying a metric of non-negative scalar curvature, then either the Dirac operator is invertible or ... 

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17.10.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

An equivariant index theorem on a Riemannian manifold.

Onirban Islam

For differential operators preserved by the action of a Lie group G, the notion of index generalises to the G-index. A prototype of this situation arises for spin-Dirac operators on a compact... 

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25.07.2024, 16:30  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Dirac eigenvalues, hyperspherical radius and applications

Christian Bär (UP)

I will explain an eigenvalue estimate for Dirac operators in terms of the hyperspherical radius of the underlying manifold. When combined with other known eigenvalue estimates this has a number of... 

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18.07.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Witten index and spectral shift function

Florian Hanisch

The spectral shift function is an object from scattering theory. It was invented to describe/compute traces of certain operators and generalizes the notion of spectral flow. It is moreover closely... 

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11.07.2024, 16:15 Uhr  –  1.10
Forschungsseminar Differentialgeometrie

LEAN 4 proof assistant: first steps

Christoph Stephan

I will give an introduction to the Lean 4 proof assistant, focusing on basics of interactive theorem proving, dependend type theory and its applications in mathematics. The talk will be suitable for... 

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04.07.2024, 16:15  –  Raum 1.10 und per Zoom
Forschungsseminar Differentialgeometrie

Timelike Ricci bounds and Einstein's theory of gravity in a non smooth setting: an optimal transport approach

Andrea Mondino (Oxford)

Optimal transport tools have been extremely powerful to study Ricci curvature, in particular Ricci lower bounds in the non-smooth setting of metric measure spaces (which can be been as a non-smooth... 

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27.06.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Fill-ins, Dirac eigenvalues and the hyperspherical radius

Christian Bär (UP)

Let be an n-dimensional closed Riemannian spin manifold. A fill-in of is a compact (n+1)-dimensional Riemannian spin manifold whose boundary is . If has nonnegative scalar... 

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20.06.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Green Operators on Static Spacetimes with Timelike Boundary

Onirban Islam

I shall introduce the Chazarain method to construct retarded and advanced Green operators for a Dirac operator on a globally hyperbolic spacetime with timelike boundary.

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23.05.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Transgressions of Characteristic Classes

Alberto Richtsfeld (UP)

In this talk I will report on my progress in computing the transgression forms for characteristic classes. First, I will compute the transgression form of characteristic classes of power sum symmetric... 

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16.05.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Rigidity of initial data sets in Minkowski space

Christian Bär (UP)

If M is a spacelike hypersurface of a Lorentzian manifold, then M inherits an induced Riemannian metric g and a second fundamental form q. The triple (M,g,q) is then called the induced initial data... 

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25.04.2024, 16:15  –  Raum 1.10
Forschungsseminar Differentialgeometrie

Atiyah-Singer-Indexsatz

Lennart Ronge (UP)

Vorbereitung auf das Blockseminar "Geometrie" nach dem Inverted-Classroom-Prinzip.
Indexsatz, Chern-Klassen, Pontrjagin-Klassen (3.4 - 4.3.7 im Skript)

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