Discrete Geometry III
Lecturer: Prof. Raman Sanyal
Contents.
Dissecting polytopes and polyhedra have many practical applications including volume computation, Ehrhart theory, and the like. Dissecting or better subdividing polytopes has a rich combinatorial theory. In the course Discrete Geometry III we will focus on ways to dissect, subdivide and decompose discrete geometric objects. Among other things we will see
- methods for triangulating point configurations (barycentric, pulling, pushing, Delaunay)
- (coherent) induced subdivisions as a unifying principle
- combinatorics of subdivisions
- moduli spaces (secondary/fiber polytopes, type cones)
- many many applications to other areas of mathematics.
The course is intended for people with a good background in discrete and convex geometry (representations of polytopes and polyhedra, combinatorics of face lattices, etc.) from, for example, Discrete Geometry I & II.
Schedule.
| Lectures | Thursday 10-12 | Arnimallee 2, seminar room | |
| Tutorial | Tuesday 10-12 | Arnimallee 2, seminar room | |
| Oral exams | Week |
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Exercises and oral exams.
There will be weekly exercise sheets. The exercises will not be corrected. The solutions are discussed (not presented!) in the weekly exercise sessions. For the regelmäßige+aktive Teilnahme, you have to attend the exercise sessions regularily and you have to participate actively.
There will be oral exams in the first week after classes.
Literature.
There will be handwritten lecture notes.
- Beck-Sanyal, "Combinatorial reciprocity theorems : an invitation to enumerative geometric combinatorics" Book eBook
- Gelfand et al, "Discriminants, resultants, and multidimensional determinants" Book
- Barvinok, "A course in convexity" Book
- De Loera et al, "Triangulations: structures for algorithms and applications" Book
- Ziegler, "Lectures on polytopes" Book