After successful completion of the course, students are able to explain the basic notions of convex geometry and proof their fundamental results (Theorem of Brunn-Minkowski and Minkowski's existence theorem). They can analyse integral transforms of spherical functions with the help of spherical harmonics and completely solve the Shephard problem about projections of convex bodies. Finally, they are are able to use the Fourier transform to solve the Busemann-Petty problem for sections of convex bodies.

Analytic description of convex and starshaped sets, geometric inequalities for the volume of convex and starshaped sets, application of spherical harmonics and the Fourier transform in geometric analysis.

Mathematical definitions and proofs

First Meeting: March 2nd, 1.30 p.m.

Place: Besprechungszimmer, Wiedner Hauptstraße 8-10, 1040 Wien, Turm A, 7.Stock

Oral Exam

Lecture notes for this course are available.