Welcome to the 20th Meetup of KW Intersections, an impressive milestone in the history of our Meetup. Thank you very much for everyone who has spoken and attended one of our meetups and we look forward to everyone who will speak at and attend our future meetups. As always we will have a mind-filling program. We will have two talks in the next meetup, presented by two of our longest serving members and co-organizers, Steven Taschuck and Stephen Paul Weber.
Phase transition in random graphs by Steven Taschuck (http://www.amotlpaa.org/), Ph.D.
Phase transition in graphs is about how the (typical size) of the largest component in a random graph varies with the probability of edges being in the graph. It’s called a “phase transition” because the component size doesn’t vary smoothly, but makes jumps between different regimes, with the effect that the graph kind of “freezes solid” as the edge probability passes a certain value and (typically) all the components suddenly merge together.
The phenomenon was discovered in 1960 by Erdos and Renyi. Steven will present a recent (2012) simple proof (http://arxiv.org/abs/1201.6529) by Krivelevich and Sudakov, which proceeds by analyzing depth-first search in a clever way.
Second talk by Stephen Paul Weber (https://singpolyma.net/) will be announced shortly.