[Facets-of-complexity] Invitation to Monday Colloquium - June 4th 2018

[Ita Brunke <i.brunke@inf.fu-berlin.de>]

You are cordially invited to our next Monday Colloquium on June 4th at 14:15 h at TU Berlin.

Speaker: Andrew Newman (Ohio State University)

Title: Small simplicial complexes with large torsion in homology

Time: Monday, June 4th - 14:15 h

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Abstract:
From Kalai's classic paper generalizing Cayley's tree-enumeration formula to simplicial complexes, it is known that simplicial complexes on a small number of vertices can have enormous torsion in homology. Moreover, in a random setting one may find instances of this phenomenon such as, for example, a 3-dimensional simplicial complex on 30 vertices with the torsion subgroup of the second homology group having order larger than 10^⁸². In this talk I will discuss the problem of explicitly constructing such complexes. In particular, I will discuss my work to use the probabilistic method to construct optimally small (up to a constant factor from a known lower bound) simplicial complexes with prescribed torsion in homology. I will also discuss an application of this work to the problem of counting homotopy types of simplicial complexes.

Exceptionally, there will be no lecture and only this colloquium.

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Graduiertenkolleg 'Facets of Complexity' www.facetsofcomplexity.de/monday