Seminar Continuous Combinatorics
Tuesdays, 14:25 at Arnimallee 2 (Villa), seminar room
In this seminar we will work through the book Introduction to Geometric Probability by Dan Klain and Gian-Carlo Rota. Despite the name, the book is not so much about probabiliy theory but, as the authors say themselves, more of an introduction to Continuous Combinatorics.
So, if you want to know
- why Grassmannians are continuous analogs of the set of all k-subsets of an n-set
- why volume, surface area, mean width, etc. are continuous analogs of f-vectors
- some extremal set theory for (flags of) subspaces
- that the vector space of rigid-motion invariant valuations is finite dimensional (Hadwiger's theorem)
- what all this has to do needles and planks and
- much more fascinating stuff about the interplay of combinatorics, convex geometry and (a tiny bit of) measure theory,
then do come to the seminar!
Rules of the Game.
- Presentation 60min., followed by a discussion about the subject at hand and about the presentation.
- Written draft outline (4 pages) to be handed in 2 weeks before the actual presentation; contains structure -- at what point which definitions/results/examples, as well as proof ideas.
- It goes without saying that you attend and actively participate during the other presentations.
|13.10.2015||Buffon Needle Problem -- intro to the whole thing||1||Raman|
|20.10.2015||Valuation and integral||2||Kathlen|
|27.10.2015||Subsets of finite set||3.1||Manuel|
|03.11.2015||Valuations on simplicial complex / discrete Helly||3.2/3||Florian|
|10.11.2015||Intrinsic volumes of parallelotopes||4||Christoph|
|17.11.2015||Lattice of polyconvex sets & Grömer's extension theorem||5.1/2||Fabian|
|24.11.2015||Helly, Klee & Cauchy||5.3-5||Giulia|
|01.12.2015||Lattice of subspaces & flag coefficients||6.1-3||Josue|
|08.12.2015||Sperner, Meshalkin & Helly||6.4-6||Tony|
|15.12.2015||Intrinsic volumes for polyconvex sets||7.1/2||Clement|
|05.01.2015||Euler relation and projection formula||7.3/4||Philip|
|12.01.2016||Characterization of volume||8.1-3||Lauri|
|19.01.2016||Normalization \& discrete volume||8.4-6||Tobias|
|02.02.2016||Intrinsic volumes on products||9.7-9||Christian|
|09.02.2016||Kinematic formulas for polyconvex sets||10||Alex Engström|