math_groups_discgeom

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.

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