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.

Date	Title	Chapter	Speaker
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
26.01.2016	Hadwiger's characterization	9.1-6	Alexander
02.02.2016	Intrinsic volumes on products	9.7-9	Christian
09.02.2016	Kinematic formulas for polyconvex sets	10	Alex Engström