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DTSTAMP:20241106T210144Z
UID:1715155200@ist.ac.at
DTSTART:20240508T100000
DTEND:20240508T110000
DESCRIPTION:Speaker: Roy Meshulam\nhosted by Matthew Kwan\nAbstract: In rec
ent years there is a growing interest in higher dimensional random complex
es\, both as natural extensions of random graphs\, and as potential tools
for new applications. We will focus on relatively new models of random com
plexes and their generic topological properties:1. A classical theorem of
Alon and Roichman asserts that the Cayley graph C(G\,S) of a group G with
respect to a logarithmic size random subset S of G is a good expander. We
consider a k-dimensional analogue of Cayley graphs\, called Balanced Cayle
y Complexes\, discuss the spectral gap of their (k-1)-Laplacian and in par
ticular obtain a high dimensional version of the Alon-Roichman theorem.2.
A permutation complex is the order complex of the intersection of two line
ar orders. We describe some properties of these complexes and discuss boun
ds on the probability that a permutation complex associated with random or
ders is topologically k-connected.Joint work with Omer Moyal.3. A classica
l result of Erdos and Gallai asserts that a graph G=(V\,E) with |E|> k(|V|
-1)/2 must contain a simple cycle of length at least k+1. We describe a hi
gh dimensional qualitative version of this result and discuss some questio
ns that arise in the random setting.Joint work with Ilan Newman and Yuri R
abinovich.
LOCATION:Moonstone Seminar Room C\, ISTA
ORGANIZER:omerhalil.unal@ist.ac.at
SUMMARY:Roy Meshulam: Aspects of Random Simplicial Complexes
URL:https://talks-calendar.ista.ac.at/events/4950
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