Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


Studying Curved Spaces


Freiburg mathematician Sebastian Goette is awarded funding from the Simons Foundation

The Freiburg mathematician Prof. Dr. Sebastian Goette will receive a total of 650,000 US dollars in funding over the coming four years for his involvement in the project “Special Holonomy in Geometry, Analysis, and Physics.” The funding is being provided by the Simons Foundation, a non-profit organization in the USA that supports fundamental research in mathematics and natural sciences.

The sketch describes an "extra twisted connected sum," a special G2 manifold. Below it is a formula for its extended nu-invariant.

Photo: Sebastian Goette

Director of the project is the mathematics professor Robert Bryant from Duke University, USA. Other collaborators include researchers from Stony Brook University and University of California in the USA and Imperial College London, King's College London, University of Bath, and University of Oxford in England.

The project focuses on Riemannian manifolds with special holonomy. These are spaces whose curves have special properties, in particular the so-called Calabi–Yau, G2, and spin(7) manifolds. These spaces fulfill the Einstein equations in vacuum, meaning that a universe without matter could take on their shape. In physics, they are needed to establish a connection between various string theories in ten dimensions or the M-theory in eleven dimensions and the space–time continuum.

Described in Albert Einstein’s general theory of relativity, the space–time continuum is the unification of space and time in a single four-dimensional structure. The string theories and the M-theory, which was developed on the basis of the former, are regarded as a promising approach for resolving the theoretical incongruities between quantum physics and the general theory of relativity.

“From a mathematical standpoint, Riemannian manifolds with special holonomy are spaces with an especially beautiful geometry,” says Goette. The goal of the collaboration is to construct more examples of such spaces and to gain further insight on the relationship between their geometrical and physical properties as well as these properties themselves. “The Freiburg subproject focuses on G2 manifolds, which are necessary for M-theory,” says Goette. “We are studying global geometrical properties and using them to compare various constructions of G2 manifolds.”

James Simons, an American mathematician, hedge-fund manager, and CO-founder of the Simons Foundation, with his wife, Marilyn Simons, also dealt with special holonomy in his 1962 doctoral dissertation.

Further information:

Prof. Dr. Sebastian Goette
Institute of Mathematics
University of Freiburg
Phone: +49 (0)761/203-5571

Weitere Informationen:

Rudolf-Werner Dreier | Albert-Ludwigs-Universität Freiburg im Breisgau

More articles from Physics and Astronomy:

nachricht Hubble sees Neptune's mysterious shrinking storm
16.02.2018 | NASA/Goddard Space Flight Center

nachricht Supermassive black hole model predicts characteristic light signals at cusp of collision
15.02.2018 | Rochester Institute of Technology

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Demonstration of a single molecule piezoelectric effect

Breakthrough provides a new concept of the design of molecular motors, sensors and electricity generators at nanoscale

Researchers from the Institute of Organic Chemistry and Biochemistry of the CAS (IOCB Prague), Institute of Physics of the CAS (IP CAS) and Palacký University...

Im Focus: Hybrid optics bring color imaging using ultrathin metalenses into focus

For photographers and scientists, lenses are lifesavers. They reflect and refract light, making possible the imaging systems that drive discovery through the microscope and preserve history through cameras.

But today's glass-based lenses are bulky and resist miniaturization. Next-generation technologies, such as ultrathin cameras or tiny microscopes, require...

Im Focus: Stem cell divisions in the adult brain seen for the first time

Scientists from the University of Zurich have succeeded for the first time in tracking individual stem cells and their neuronal progeny over months within the intact adult brain. This study sheds light on how new neurons are produced throughout life.

The generation of new nerve cells was once thought to taper off at the end of embryonic development. However, recent research has shown that the adult brain...

Im Focus: Interference as a new method for cooling quantum devices

Theoretical physicists propose to use negative interference to control heat flow in quantum devices. Study published in Physical Review Letters

Quantum computer parts are sensitive and need to be cooled to very low temperatures. Their tiny size makes them particularly susceptible to a temperature...

Im Focus: Autonomous 3D scanner supports individual manufacturing processes

Let’s say the armrest is broken in your vintage car. As things stand, you would need a lot of luck and persistence to find the right spare part. But in the world of Industrie 4.0 and production with batch sizes of one, you can simply scan the armrest and print it out. This is made possible by the first ever 3D scanner capable of working autonomously and in real time. The autonomous scanning system will be on display at the Hannover Messe Preview on February 6 and at the Hannover Messe proper from April 23 to 27, 2018 (Hall 6, Booth A30).

Part of the charm of vintage cars is that they stopped making them long ago, so it is special when you do see one out on the roads. If something breaks or...

All Focus news of the innovation-report >>>



Industry & Economy
Event News

2nd International Conference on High Temperature Shape Memory Alloys (HTSMAs)

15.02.2018 | Event News

Aachen DC Grid Summit 2018

13.02.2018 | Event News

How Global Climate Policy Can Learn from the Energy Transition

12.02.2018 | Event News

Latest News

Fingerprints of quantum entanglement

16.02.2018 | Information Technology

'Living bandages': NUST MISIS scientists develop biocompatible anti-burn nanofibers

16.02.2018 | Health and Medicine

Hubble sees Neptune's mysterious shrinking storm

16.02.2018 | Physics and Astronomy

Science & Research
Overview of more VideoLinks >>>