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DESCRIPTION: From Kalai's classic paper generalizing Cayley's tree-enumerat
 ion formula to simplicial complexes\, it is known that simplicial complexes
  on a small number of vertices can have enormous torsion in homology. Moreo
 ver\, 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 su
 ch complexes. In particular\, I will discuss my work to use the probabilist
 ic method to construct optimally small (up to a constant factor from a know
 n 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.  
DTSTAMP:20181105T173500
DTSTART:20180604T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
 es 17. Juni 136\n 10623 Berlin\n room MA 041 (ground floor)
SEQUENCE:0
SUMMARY:Andrew Newman (Ohio State University): Small simplicial complexes w
 ith large torsion in homology
UID:89312371@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20180604-C-Newman.html
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