VL: Discrete Geometry II (Winter 2025/26)
This is a BMS Area 5 Core Course.
It continues Discrete Geometry I.
The exercise (UE) and tutorial (Tut) sessions will be given by Marcel Wack.
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Contents
This course will discuss more advanced topics in polyhedral geometry, with a view toward plane algebraic curves.
This will also include a first glimpse of tropical geometry.
Prerequisites: Discrete Geometry I (linear optimization, polytopes, convex hull algorithms); basic undergraduate algebra (it is useful to know that ideals in polynomial rings are finitely generated).
- Regular subdivisions of point configurations
- Tropical hypersurfaces
- Tropical plane curves
- Plane algebraic curves, over various fields
- Real plane algebraic curves
- Secondary cones and secondary fans
References
- De Loera, Rambau and Santos: Triangulations. Springer, 2010.
- Gelfand, Kapranov and Zelevinsky: Discriminants, resultants, and multidimensional determinants. Springer, 1994.
- Joswig: Essentials of tropical combinatorics. AMS, 2021.
- Joswig and Theobald: Polyhedral and algebraic methods in computational geometry. Springer, 2013.
- Maclagan and Sturmfels: Introduction to tropical geometry. AMS, 2015.