Convex Geometry schedule

Week 1  (February 12) Affine subspaces, affine combinations, convex sets, convex combinations.
Week 2  (February 19) Convex hull, theorems of Radon and Carathéodory.
Week 3  (February 26) Helly's theorem, hyperplanes, linear functionals.
Week 4  (March 5) Minkowski addition, separation.
Week 5  (March 12) Supporting hyperplanes, faces of a convex set, extremal and exposed points, the Krein-Milman theorem.
Week 6  (March 19) Algebra of convex sets, valuations.
Week 7  (March 26) 1st midterm, Euler characteristic.
Week 8  (April 2) Good Friday, Spring break.
Week 9  (April 9) Polytopes, polyhedral sets, their face structures.
Week 10  (April 16) Euler's theorem for polytopes.
Week 11 (April 23) Polarity, duality theorem for polytopes.
Week 12 (April 30) 2nd midterm, a special class of polytopes: cyclic polytopes.
Week 13  (May 7) Distance of convex bodies: Hausdorff and Banach-Mazur distance.
Week 14  (May 14) 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.