On the Maurer-Cartan Equation (Julian Holstein, UHH)

The innocuous-looking Maurer-Cartan equation $\mathrm{d}\omega + \frac 1 2 [\omega, \omega] = 0$ was discovered as a property of certain forms in differential geometry more than 100 years ago. Today it plays an important role throughout mathematics and in theoretical physics. It describes flat connections, mediates algebraic dualities, characterises deformations in algebra and geometry, and appears as the quantum master equation in Lagrangian gauge theory. I will describe how the Maurer-Cartan equation combines homological and algebraic structures, and give examples of its use in modern mathematics.

Laser interferometry on ground and in space for gravitational wave astronomy (Oliver Gerberding, UHH)

Space-time is wiggling and we have started to listen. The direct detection of gravitational waves opens up a new window to astronomy, cosmology and fundamental physics, giving us a new way to observe events with energies and masses unreachable in ground-based experiments. The ongoing detections by the LIGO and Virgo detectors and our current understanding of the gravitational wave spectrum give experimentalists a clear task: We have to develop sensors with lower noise and with sensitivities at lower frequencies. Our most important tool is laser interferometry, the underlying technique of currently planned detectors. To reach the design sensitivities of 3rd generation ground based detectors, like Einstein telescope, and space-based detectors, like the Laser Interferometer Space Antenna (LISA), we have to study and improve laser interferometry and all of its associated aspects and components. Developing new instruments and techniques that are compatible with the unique environments of each detector is an international effort with various groups focusing on different aspects. The newly established research group for gravitational wave detection at the University of Hamburg studies techniques that make use of advances in digital signal processing and material sciences, for example by using LISA-like multi-fringe interferometry in a compact form as local sensors for future ground-based detectors.

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Slides Holstein (1.6 MB)

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Slides Gerberding (33.8 MB)

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