Date: May 04, 2026
Time: 04:00 PM
Venue: Lecture Hall 1003, Block 7, IISER Berhampur
Flyer Link: Click here to view
"Approaching a problem on control through modern geometry"
It is known, in the theory of control of systems comprising interconnected devices or machines, each of whose outputs depend linearly on their inputs, that the ability to stabilize such a system is associated with a type of interpolation problem. The strategy for its solution is very different from strategies arising from Lagrange interpolation due to the constraints imposed by the target spaces: the classical Cartan domains. It was shown in the 2000s that for a system in which only a few, but not all, of the system parameters are prone to uncertainties, its stabilization is more efficiently understood in terms of a complex-analytic interpolation problem into the "unit ball" determined by a non-negative function called the structured singular value. The geometry of such domains further vitiates the interpolation problem. Interestingly, these "unit balls" are invariant under the action of certain classical Lie groups. Thus, the problem of understanding the existence of interpolants can be approached via an aspect of algebraic geometry known as Geometric Function Theory (GIT). In this talk, however, we will see how some of the existence results can be understood using just linear algebra and the basic theory of complex-analytic functions.
Prof. Gautam Bharali - Prof. Gautam Bharali is a versatile mathematician working in the field of several complex variables. Prof. Bharali did his PhD from University of Wisconsin, USA in 2002. Before moving to the Indian Institute of Science, where he is a professor now, he worked as an assistant professor at the University of Wisconsin. He was an associate of the International Centre for Theoretical Physics, Italy from 2007-2013. Prof. Bharali was awarded the INSA medal for young scientist in 2009. In 2015, he was awarded the Swarnajayanti Fellowship. Prof. Bharali is a fellow of Indian Academy of Science.
