Equivariant Methods in Discrete Geometry: Problems and Progress
Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017
Location: MSRI: Simons Auditorium
55N91 - Equivariant homology and cohomology [See also 19L47]
In this lecture, I will discuss three different problems from Discrete Geometry,
- the Topological Tverberg Problem,
- the Colored Tverberg Problem, and
- the Grünbaum Hyperplane Problem.
These problems have many things in common:
- They are easy to state, and may look harmless,
- They have very nice and classical configuration spaces,
- they may be attacked by ``Equivariant Obstruction Theory'',
- this solves the problems --- but only partially,
- which leads us to ask more questions, look for new tools ...
- and this yields surprising new results.
(Joint work with Pavle Blagojevic, Florian Frick, Albert Haase, and Benjamin Matschke)
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