BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Érika Roldán (Max Planck Institute for Mathematics in the Scienc
 es (MiS) Leipzig - Germany)
DTSTART:20230127T160000Z
DTEND:20230127T170000Z
DTSTAMP:20260423T041525Z
UID:GEOTOP-A/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GEOTOP-A/34/
 ">Topology of random 2-dimensional cubical complexes</a>\nby Érika Roldá
 n (Max Planck Institute for Mathematics in the Sciences (MiS) Leipzig - Ge
 rmany) as part of GEOTOP-A seminar\n\n\nAbstract\nWe study a natural model
  of random 2-dimensional cubical complexes which are subcomplexes of an n-
 dimensional cube\, and where every possible square (2-face) is included in
 dependently with probability p. Our main result exhibits a sharp threshold
  $p=1/2$ for homology vanishing as the dimension n goes to infinity. This 
 is a 2-dimensional analogue of the Burtin and Erdős-Spencer theorems char
 acterizing the connectivity threshold for random graphs on the 1-skeleton 
 of the n-dimensional cube. Our main result can also be seen as a cubical c
 ounterpart to the Linial-Meshulam theorem for random 2-dimensional simplic
 ial complexes. However\, the models exhibit strikingly different behaviors
 . We show that if $p > 1 - √1/2 ≈ 0.2929$\, then with high probability
  the fundamental group is a free group with one generator for every maxima
 l 1-dimensional face. As a corollary\, homology vanishing and simple conne
 ctivity have the same threshold. This is joint work with Matthew Kahle and
  Elliot Paquette.\n
LOCATION:https://researchseminars.org/talk/GEOTOP-A/34/
END:VEVENT
END:VCALENDAR