Integral Geometry of Cones

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Title

Integral Geometry of Cones

Group Numerical Analysis and Scientific Computing
Supervisor
Description

Science and technology depends increasingly on the efficient acquisition, storage and processing of vast amounts of data.
While the seemingly endless availability of data is a blessing from a statistical point of view, it poses enormous challenges from a computational perspective.

An exciting recent development has been the emergence of ideas for efficient information acquisition and identification that take advantage of simple underlying structure of the problems considered . This new genre of ideas, encompassing the burgeoning field of compressed sensing, has experienced tremendous growth in recent years.

Numerical optimization plays an important role in these developments, and its effectiveness depends crucially on deep geometric properties of the underlying problems. I am interested in studying such problems in convex geometry and geometric probability that help explain the reach and limitations of convex optimization. Besides background in numerical analysis, this project would also benefit from knowledge in computational complexity, differential geometry, and probability.

Literature:
{\bf Schneider, Weil}, Stochastic and Integral Geometry.
{\bf Foucart, Rauhut}, A Mathematical Introduction to Compressive Sensing.

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