Convex Geometry schedule

Week 1  (March 3) Affine subspaces, affine combinations, convex sets, convex combinations.
Week 2  (March 10) Convex hull, theorems of Radon and Carathéodory.
Week 3  (March 17) Helly's theorem, hyperplanes, linear functionals.
Week 4  (March 24) Minkowski addition, separation.
Week 5  (March 31) Supporting hyperplanes, faces of a convex set, extremal and exposed points, the Krein-Milman theorem.
Week 6  (April 7) Good Friday, Spring break
Week 7  (April 14) 1st midterm, Algebra of convex sets, valuations. Euler characteristic.
Week 8  (April 21) Polytopes, polyhedral sets, their face structures.
Week 9  (April 28) .Euler's theorem for polytopes.
Week 10  (May 5) no class (classes according to eventh week Mondays)
Week 11 (May 12) Polarity, duality theorem for polytopes.
Week 12 (May 19) 2nd midterm, a special class of polytopes: cyclic polytopes.
Week 13  (May 26) Distance of convex bodies: Hausdorff and Banach-Mazur distance.
Week 14  (June 2) Ellipsoids, the Löwner-John ellipsoid.


Problem sheets and other information


Recommended literature:

[1] R. Tyrrell Rockafellar: Convex Analysis, Princeton University Press, Princeton NJ, 1972.

[2] Alexander Barvinok: A Course in Convexity, Graduate Studies in Mathematics 54, Amer. Math. Soc., Providence RI, 2002.

[3] Jiři Matoušek: Lectures in Discrete Geometry, Graduate Texts in Mathematics 212, Springer, New York, 2002.

[4] Branko Grünbaum, Convex polytopes, Graduate Texts in Mathematics 221, Springer, New York, 2003.