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Combinatorial Topology and Applications

International Workshop

Date: Friday, September 12th, 2014,
Time: 09:00-14:00
Place: Universität Bremen, MZH 7200

Emanuele Delucchi (Université de Fribourg)
Michał Adamaszek (MPI Informatik, Saarbrücken)
Dmitry Feichtner-Kozlov (Universität Bremen)


09:00-10:00Emanuele Delucchi (Université de Fribourg)
Recent developments in toric arrangements
The study of toric arrangements is rooted in the literature in both its topological (since at least Looienga in 1993) and combinatorial aspects (e.g., Ehrenborg, Readdy and Slone 2009). Recent work of De Concini, Procesi and Vergne provided a fresh impulse towards a comprehensive study of this subject, viewed as a generalization of the successful theory of hyperplane (or subspace) arrangements in vector spaces. Out of this impulse grew many new results and techniques, concerning both topology and in combinatorics, which I will try to survey with an eye towards setting up a general combinatorial-topological framework which might lead to the treatment of even more general types of arrangements. Some of the results I will present have been obtained in joint works with Karim Adiprasito, Filippo Callegaro, Giacomo d'Antonio or Sonja Riedel.
10:30-11:30Michał Adamaszek (MPI Informatik, Saarbrücken)
Arcs on a circle
For any finite collection of arcs on a circle we show that its nerve is homotopy equivalent to an odd sphere or a wedge of even spheres. A key role is played by certain simplicial complexes N(n,k) with cyclic symmetry. I will mention some results and conjectures about the topology of these complexes, their relation to the classical cyclic polytopes and an unexpected connection to an extremal problem about the gaps between roots of trigonometric polynomials.
Joint with Henry Adams, Florian Frick, Christopher Peterson, Corrine Previte.
11:45-12:45Dmitry Feichtner-Kozlov (Universität Bremen)
Conguration spaces arising in distributed computing
In this talk we shall describe a family of simplicial complexes, called protocol complexes, which arise naturally as some of the central objects in the eld of theoretical distributed computing. These complexes give a description of the totality of all possible executions of distributed protocols in a xed computational model. They are the natural analog of conguration spaces in this context. Part of the talk will be based in the recent book "Distributed Computing through Combinatorial Topology", joint with M. Herlihy and S. Rajsbaum.

Copyright: ALTA, 2014.