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SUMMARY:Radmila Sazdanović (NCSU)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260423T024740Z
UID:TG_ET/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TG_ET/6/">Bi
 g data and applied topology methods in knot theory</a>\nby Radmila Sazdano
 vić (NCSU) as part of Topology and geometry: extremal and typical\n\n\nAb
 stract\nA multitude of knot invariants\, including quantum invariants and 
 their categorifications\, have been introduced to aid with characterizing 
 and classifying knots and their topological properties. Relations between 
 knot invariants and their relative strengths at distinguishing knots are s
 till mostly elusive. We use Principal Component Analysis (PCA)\, Ball Mapp
 er\, and machine learning to examine the structure of data consisting of v
 arious polynomial knot invariants and the relations between them. Although
  of different origins\, these methods confirm and illuminate similar subst
 ructures in knot data. These approaches also enable comparison between num
 erical invariants of knots such as the signature and s-invariant via their
  distribution within the Alexander and Jones polynomial data. Although thi
 s work focuses on knot theory the ideas presented can be applied to other 
 areas of pure mathematics and possibly in data science. The hybrid approac
 h introduced here can be useful for infinite data sets where representativ
 e sampling is impossible or impractical.\n
LOCATION:https://researchseminars.org/talk/TG_ET/6/
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