Convex Geometry schedule

Week 1  (February 18) Affine subspaces, affine combinations, convex sets, convex combinations.
Week 2  (February 25) Convex hull, theorems of Radon and Carathéodory.
Week 3  (March 4) Helly's theorem, hyperplanes, linear functionals.
Week 4  (March 11) Minkowski addition, separation.
Week 5  (March 18) Supporting hyperplanes, faces of a convex set, extremal and exposed points, the Krein-Milman theorem.
Week 6  (March 25) Algebra of convex sets, valuations.
Week 7  (April 1) 1st midterm, Euler characteristic.
Week 8  (April 8) Polytopes, polyhedral sets, their face structures.
Week 9  (April 15) Good Friday, Spring break.
Week 10  (April 22) Euler's theorem for polytopes.
Week 11 (April 29) Polarity, duality theorem for polytopes.
Week 12 (May 6) 2nd midterm, a special class of polytopes: cyclic polytopes.
Week 13  (May 13) Distance of convex bodies: Hausdorff and Banach-Mazur distance.
Week 14  (May 20) 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.