Advanced Networks Colloquium: Yuliy Baryshnikov, "Complexity of dodging a bullet"
Friday, April 1, 2016
1146 AV Williams Building
The Advanced Networks Colloquium
Complexity of dodging a bullet: on the topology of the space of directed paths
Electrical and Computer Engineering
University of Illinois Urbana-Champaign
Roundtable: 3:00 p.m., 2168 AV Williams Bldg.
Directed paths appear in several areas of science and engineering, from control theory to physics to computer sciences. Most prominent setting describes in terms of the directed paths the space of execution of concurrent programs subject to non-collision constraints, yet the model of a vehicle avoiding (stationary or moving) obstacles is perhaps the easiest to grasp. While the (conventional) spaces of paths are a key tool of algebraic topology, the directed path spaces remain their exotic relatives: their topology till recently resisted any constructive characterization. In this talk I show how to address the question of understanding the topology of the space of obstacle avoiding oriented paths, as well as show their relevance in control and networks.
Yuliy Baryshnikov grew up in Moscow, then in Soviet Union, and got his PhD in applied mathematics, from Institute of Control Sciences in Moscow, in 1987. He spent his Humboldt Research Fellowship University of Osnabruck in Germany, and then worked as a faculty member in the Netherlands, UK and France, before joining Bell Labs in Murray Hill, NJ in 2001. In 2011 he resigned from his position as a department head there and moved West, to become professor of mathematics and electrical and computer engineering at the University of Illinois at Urbana-Champaign. His research interests include probability theory, singularities, dynamical systems, and combinatorics. Among applied areas his favorites are sensor networks, nonlinear control, mathematical economics, self-assembly.