Colloquia
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Fri, 04/05/2012 16:30 |
Professor Steven Strogatz (Cornell University) |
Colloquia  |
L2 |
| Consider a fully-connected social network of people, companies,or countries, modeled as an undirected complete graph with real numbers onits edges. Positive edges link friends; negative edges link enemies.I'll discuss two simple models of how the edge weights of such networksmight evolve over time, as they seek a balanced state in which "the enemy ofmy enemy is my friend." The mathematical techniques involve elementaryideas from linear algebra, random graphs, statistical physics, anddifferential equations. Some motivating examples from internationalrelations and social psychology will also be discussed. This is joint workwith Seth Marvel, Jon Kleinberg, and Bobby Kleinberg. | |||
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Fri, 08/06/2012 16:30 |
Bruce Kleiner (NYU) |
Colloquia |
L2 |
| A map betweem metric spaces is a bilipschitz homeomorphism if it is Lipschitz and has a Lipschitz inverse; a map is a bilipschitz embedding if it is a bilipschitz homeomorphism onto its image. Given metric spaces X and Y, one may ask if there is a bilipschitz embedding X—>Y, and if so, one may try to find an embedding with minimal distortion, or at least estimate the best bilipschitz constant. Such bilipschitz embedding problems arise in various areas of mathematics, including geometric group theory, Banach space geometry, and geometric analysis; in the last 10 years they have also attracted a lot of attention in theoretical computer science. The lecture will be a survey bilipschitz embedding in Banach spaces from the viewpoint of geometric analysis. | |||
