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DTSTAMP:20260427T100745Z
UID:5996c8ac05f33818838575@ist.ac.at
DTSTART:20171019T134500
DTEND:20171019T144500
DESCRIPTION:Speaker: Anton Nikitenko\nAbstract: The main objects considered
  in the present work are simplicial and CW-complexes with vertices forming
  a random point cloud. In particular\, we consider Poisson point process i
 nRn and study Delaunay and Voronoi complexes of the first and higher order
 s and weighted Delaunay complexes obtained as sections of Delaunay complex
 es\, as well as the Cech complex.Further\, we examine the Delaunay complex
  of a Poisson point process on the sphere Sn\, as well as of a uniform poi
 nt cloud\, which is equivalent to the convex hull\, providing a connection
  to the theory of random polytopes. Each of the complexes in question can 
 be endowed with a radius function\, which maps its cells to the radii of a
 ppropriately chosen circumspheres\, called the circumradius of the cell. A
 pplying and developing discrete Morse theory for these functions\, joining
  it together with probabilistic and sometimes analytic machinery and devel
 oping several integral geometric tools\, in all cases we are able to obtai
 n up to constants the distribution of radii of typical intervals of all ty
 pes\, which also provides the distribution of circumradii of a typical cel
 l of the complex. In low dimensions the constants can be computed explicit
 ly\, thus providing the explicit expressions for the expected numbers of c
 ells. In particular\, it allows to find the expected density of simplices 
 of every dimension for a Poisson point process on R4\, whereas the result 
 for R3 was known already in 1970s
LOCATION:Mondi Seminar Room 2\, Central Building\, ISTA
ORGANIZER:useiss@ist.ac.at
SUMMARY:Anton Nikitenko: Discrete Morse Theory for Random Complexes
URL:https://talks-calendar.ista.ac.at/events/888
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