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SUMMARY:Chung-Ping Lai (Oregon State University)
DTSTART:20250709T103000Z
DTEND:20250709T113000Z
DTSTAMP:20260422T140237Z
UID:BilTop/118
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/118/"
 >Homology of Simplicial G-complexes and Group Rings</a>\nby Chung-Ping Lai
  (Oregon State University) as part of Bilkent Topology Seminar\n\nLecture 
 held in SA 141.\n\nAbstract\nThere has been a growing trend to use the hom
 ology of simplicial complexes to study complex data structures because of 
 its resilience to deformation and noise.  In this talk\, we investigate th
 e question of how one can recover the homology of a simplicial complex X e
 quipped with a regular action of a finite group G from the structure of it
 s quotient space X/G. Specifically\, we describe a process for enriching t
 he structure of the chain complex C*(X/G\; F) using the data of a complex 
 of groups\, a framework developed by Bridson and Corsen for encoding the l
 ocal structure of a group action. We interpret this data through the lens 
 of matrix representations of the acting group\, and combine this structure
  with the standard simplicial boundary matrices for X/G to construct a sur
 rogate chain complex. In the case G = Zk\, the group ring FG is commutativ
 e and matrices over FG admit a Smith normal form\, allowing us to recover 
 the homology of G from this surrogate complex. This algebraic approach com
 plements the geometric compression algorithm for equivariant simplicial co
 mplexes described by Carbone\, Nanda\, and Naqvi.\n
LOCATION:https://researchseminars.org/talk/BilTop/118/
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