Discrete Geometry III
Winter Semester 2015/2016
times
syllabus
literature
homeworks
what happened so far
Prof. Raman Sanyal, Arnimallee 2, room 105
For office hours send us an e-mail to make an appointment.news
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First class on Tuesday, October 13.
times
| lecture | tuesday | 10:15 | Seminarraum Arnimallee 2 (Villa) |
| recitation | wednesday | 14:25 | 046/T9 Seminarraum (Takustr. 9) |
syllabus / prerequisites / formalities
This is the third in a series of three courses on discrete geometry. This advanced course centers around the `g-Theorem', that is, the complete characterization of face numbers of simplicial convex polytopes. Combining ideas from the combinatorics (Discrete Geometry I) and the convex geometry (Discrete Geometry II) of polytopes naturally leads to McMullen's polytope/weight algebra. In this setup the g-Theorem and its proof can be clearly phrased. If time permits we will also address connections of the `algebra of polytopes' to intersection theory in toric and tropical geometry.Prerequisites
Preferably Discrete Geometry I and II. Background in discrete geometry (polytopes, subdivisions, h-vectors) and convex geometry (mixed volumes, Brunn-Minkowski, Alexandrov-Fenchel) should suffice.Formalities
To successfully pass the course, you need to...- ...actively participate in the recitations,
- ...get at least 60 percent of the total number of homework points (see homeworks),
- ...present at least one of the homework problems in the recitation, and
- ...pass the exam at the end of the semester (details will be discussed in the first week).
literature
Most of the references from Discrete Geometry I and Discrete Geometry II are still available in the Semesterapparat at the math library. Further bibliography will be anounced in the lectures.homeworks
There will be about 10 homework sheets (posted here). You can write your solution to the homeworks in pairs. Please try to solve all problems. This will deepen the understanding of the material covered in the lectures. You are welcome to ask (in person or email) for additional hints for any exercise. Please think about the exercise before you ask. Please mark two of your solutions. Only these will be graded. Some problems are mandatory. You can earn 20 points on every homework sheet. You can get extra credit by solving the bonus problems. State who wrote up the solution. You have to hand in the solutions before the recitation on Wednesday. Everybody has to write up at least 25 percent of the solutions. Everybody has to present at least one problem in the recitation session.| Homework #6 | due February 10 | |
| Homework #5 | due January 20 | |
| Homework #4 | due December 16 | |
| Homework #3 | due November 25 | |
| Homework #2 | due November 11 | |
| Homework #1 | due October 28 |
what happened so far (for the lecture notes click the dates)
We are putting together a LaTeXed set of lecture notes here. Mind you, the notes are not necessary up-to-date and we don't take any responsibility errors or completeness. What happend in the lectures is what counts. However, if you find errors or short-comings, please let us know!