VL: Discrete Geometry: Polytopes and Polynomials, WS 14/15
Michael
Joswig, Institut
für Mathematik, TU
Berlin.
Assistent: Benjamin Assarf
| VL: | Tuesday | 10-12 | (MA 621) |
| Wednesday | 10-12 | (MA 621) |
| TUT+UE: | Thursday | 14-16 | (MA 751) |
Exam
The dates for the oral exam are: Wed 11th of Feb. and Wed 04th of March. Please check with Antje Schulz in MA 625
Contents
Assuming a basic background in polytope theory, this course
covers topics in polytopal combinatorics with a view towards
applications to solving systems of polynomial equations.
Subject overview:
- graphs of polytopes: simple polytopes, Balinski's theorem
- lattice points and Ehrhart polynomials
- triangulations, regular subdivisions, mixed subdivisions and mixed volume
- secondary fans
- Theorems of Bernstein, Kushnirenko and Khovanskii
- a tiny bit of toric varieties and tropical geometry
References (more to be added)
- Beck and Robins: Computing the continuous discretely. UTM. Springer, 2007.
- Cox, Little, O'Shea: Ideals, varieties, and algorithms. Third edition. UTM. Springer, 2007.
- Cox, Little, O'Shea: Using algebraic geometry. Second edition. GTM, Springer, 2005.
- De Loera, Rambau and Santos: Triangulations. Springer, 2010.
- Joswig and Theobald: Polyhedral and algebraic methods in computational geometry. Springer, 2013.
- Joswig and Ziegler: Neighborly cubical polytopes. The Branko Grünbaum birthday issue. Discrete Comput. Geom. 24, 2000
- Joswig: Reconstructing a non-simple polytope from its graph. DMV Sem., 29, 2000.
- Thomas: Lectures in geometric combinatorics. Student Mathematical Library, 33. IAS/Park City Mathematical Subseries. AMS, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ, 2006.
- Ziegler: Lectures on polytopes. GTM. Springer, 1995.
Exercise Sheets
Other
Michael Joswig
Last modified: Wed Jan 28 09:41:15 CET 2015