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Other seminars

TuesdayDec 26, 201711:15
Distinguished Lecture SeriesRoom 1
Speaker:Allen TannenbaumTitle:Optimal Mass Transport and the Robustness of Complex NetworksAbstract:opens in new windowin html    pdfopens in new window

Today's technological world is increasingly dependent upon the reliability, robustness, quality of service and timeliness of networks including those of power distribution, financial, transportation, communication, biological, and social. For the time-critical functionality in transferring resources and information, a key requirement is the ability to adapt and reconfigure in response to structural and dynamic changes, while avoiding disruption of service and catastrophic failures. We will outline some of the major problems for the development of the necessary theory and tools that will permit the understanding of network dynamics in a multiscale manner.

Many interesting networks consist of a finite but very large number of nodes or agents that interact with each other. The main challenge when dealing with such networks is to understand and regulate the collective behavior. Our goal is to develop mathematical models and optimization tools for treating the Big Data nature of large scale networks while providing the means to understand and regulate the collective behavior and the dynamical interactions (short and long-range) across such networks.

The key mathematical technique will be based upon the use optimal mass transport theory and resulting notions of curvature applied to weighted graphs in order to characterize network robustness. Examples will be given from biology, finance, and transportation.

TuesdayDec 26, 201712:30
Distinguished Lecture SeriesRoom 1
Speaker:Walter StraussTitle:Steady Water WavesAbstract:opens in new windowin html    pdfopens in new window
The mathematical study of water waves became possible after the derivation of the basic mathematical equations of fluids by Euler in 1752. Later, water waves, with a free boundary at the air interface, played a central role in the work of Poisson, Cauchy, Stokes, Levi-Civita and many others. It has seen greatly renewed interest among mathematicians in recent years. I will consider classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, one can prove that there exist many such waves. They are exact smooth solutions of the Euler equations with the physical boundary conditions. Some of the waves are quite tall and steep and some are overhanging. There are periodic ones and solitary ones. I will also exhibit some numerical computations of such waves. Many fundamental problems remain open.