Winter Term 2014/2015
Description
In this seminar we treat current research problems in discrete and computational geometry that can be approached using methods from algebraic topology. The aim of the seminar is to make advances in research and introduce students to potential research topics.
Speakers
All seminars will take place the seminar room in the Villa, Arnimallee 2, 14195 Berlin.
| Speaker | Date | Time | Title and Abstract |
|---|---|---|---|
| Aldo Guzmán Sáenz (Cinvestav, MX) | Oct 22, 2014 | 5 PM s.t. | Title: The cohomology ring away from 2 of F(RP^n,k). Abstract: In this talk we present a computation of the cohomology ring of the configuration space of k ordered points in the n-th dimensional real projective space. The strategy used for this computation allows us to compute the cohomology ring of ordered configurations in the punctured n-th dimensional real projective space. |
(U Bonn) | Oct 29, 2014 | 5:15 PM | Title: On the homology of Sullivan Diagrams. Abstract: In string topology one studies the algebraic structures of the chains of the free loop space of a manifold by defining operations on them. Recent results show that these operations are parametrized by certain graph complexes that compute the homology of compatifications of the Moduli space of Riemann surfaces. Finding non-trivial homology classes of these compactifications is related to finding non-trivial string operations. However, the homology of these complexes is largely unknown. In this talk I will describe one of these complexes: the chain complex of Sullivan diagrams. In the genus zero case, I'll give a reinterpretation of it in terms of weighted partitions, give some computational results, and if time permits, I'll describe work in progress that suggests that these are highly connected. This talk is based on joint work with F. Lutz. |
(IITP Moscow) | Nov 05, 2014 | 5PM s.t. | Title: Flexible polyhedra and their volumes. Abstract: Consider a closed polyhedral surface in the Euclidean three-space with rigid faces and with hinges at edges. If this polyhedral surface admits a deformation (a flexion) that is not induced by an ambient rotation of the space, then it is called a flexible polyhedron. A definition of a flexible polyhedron in an n-dimensional Euclidean space is completely similar. A problem on existence of flexible polyhedra turned out to be rather non-trivial. First examples of flexible polyhedra are Bricard's self-intersected flexible octahedra (1897). However, the first example of an embedded (i.e., non-self-intersected) flexible polyhedron was constructed by Connelly only in 1977. One of the most amazing facts in the theory of flexible polyhedra is Sabitov's theorem claiming that the volume of an arbitrary flexible polyhedron in the three-dimensional Euclidean space is constant during the flexion. (Earlier this assertion was known as the Bellows Conjecture.) The talk will contain a survey of recent results by the speaker concerning flexible polyhedra, and the main ideas behind these results. This will include: (1) The constructions of self-intersected flexible cross-polytopes in Euclidean and Lobachevsky spaces of all dimensions, and of embedded flexible cross-polytopes in spheres of all dimensions. In dimensions 5 and higher these are the first known examples of flexible polyhedra and in dimensions 4 and higher these are the first known examples of embedded flexible polyhedra. (2) The proof of the analogue of the Bellows Conjecture in the Euclidean spaces of arbitrary dimensions. (3) The proof of the analogue of the Bellows Conjecture in odd-dimensional Lobachevsky spaces, and the counterexamples to the Bellows Conjecture in spheres of all dimensions. (4) Results on the polyhedral relations among the entries of the Gram matrix of the period vectors for a doubly-periodic two-dimensional polyhedral surface in the three-dimensional Euclidean space. |
| -- | Nov 12, 2014 | (no talk) | |
(FU Berlin) | Nov 19, 2014 | 5PM s.t. | TBA |
(TU Berlin) | Nov 26, 2014 | 5PM s.t. | TBA |
(HU Berlin) | Dec 17, 2014 | 5PM s.t. | TBA |
Organizers
| Contact | |
| Pavle Blagojević | blagojevic(at)math.fu-berlin.de |
| Holger Reich | holger.reich(at)fu-berlin.de |
| Elmar Vogt | vogt(at)math.fu-berlin.de |
| Günter M. Ziegler | ziegler(at)math.fu-berlin.de |
