Faculty Activities[ Edit ]
Advisor: Naama Brenner
Abstract: Cellular networks exhibit pre-designed responses to many challenges, but also endow the cell with the ability to adapt and display novel phenotypes in the face of unforeseen challenges. In this seminar we will present a computational framework which attempts to describe such plasticity in random networks. We show that the convergence of this exploration in the high-dimensional space of network connections depends crucially on network topology. For large networks, convergence is most efficient for networks with scale-free out going degree distributions which are typical of cellular networks.
In order to investigate the dynamics and convergence properties of such networks we develop an approximation for scale-free networks, the STAR network, which is based on the crucial role hubs play in network dynamics.
We show that STAR networks retain many of the properties of scale-free networks and enable analytical understanding of the convergence properties exhibited in our model.
Abstract: The notion of roots is absolutely central to Lie theory and, in its classical version, very much tied to groups generated by reflections. My goal in this talk it to explore how this notion may be broadened to incorporate what is currently happening on the frontiers of Lie theory. One interesting new phenomenon, which I am hoping to discuss, is the possibility that roots and dual roots live in lattices of different rank. This makes the Langlands-like duality that exchanges them a particularly dramatic operation.
*Light refreshments on the 8th floor (faculty lounge) at 16:30*