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DTSTART;TZID=America/New_York:20210910T093000
DTEND;TZID=America/New_York:20210910T103000
DTSTAMP:20260711T090626
CREATED:20240213T114336Z
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SUMMARY:Threshold phenomena in random graphs and hypergraphs
DESCRIPTION:Member Seminar \nSpeaker: Michael Simkin \nTitle: Threshold phenomena in random graphs and hypergraphs \nAbstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics\, computer science\, and other fields. \nThe model is defined as follows: Given a natural number $n$ and a parameter $p \in [0\,1]$\, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$\, independent of all others. Despite their apparent simplicity\, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena. \nA central feature is the appearance of threshold phenomena: For all monotone properties (e.g.\, connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e.\, with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.
URL:https://cmsa.fas.harvard.edu/event/9-10-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T093000
DTEND;TZID=America/New_York:20210917T103000
DTSTAMP:20260711T090626
CREATED:20240214T080149Z
LAST-MODIFIED:20240301T112535Z
UID:10002577-1631871000-1631874600@cmsa.fas.harvard.edu
SUMMARY:Geometry\, Entanglement and Quasi Local Data
DESCRIPTION:Member Seminar \nSpeaker: Itamar Shamir \nTitle: Geometry\, Entanglement and Quasi Local Data \nAbstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.
URL:https://cmsa.fas.harvard.edu/event/9-17-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210924T093000
DTEND;TZID=America/New_York:20210924T103000
DTSTAMP:20260711T090626
CREATED:20240214T075925Z
LAST-MODIFIED:20240301T112341Z
UID:10002575-1632475800-1632479400@cmsa.fas.harvard.edu
SUMMARY:Stability and convergence issues in mathematical cosmology
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Stability and convergence issues in mathematical cosmology \nAbstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk\, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized\, one needs to study its stability properties. Therefore\, I will briefly discuss the stability issue and its consequences (e.g.\, structure formation\, etc).
URL:https://cmsa.fas.harvard.edu/event/9-24-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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