Traditionally, dynamical systems have been modelled as ordinary differential equations. A more accurate model, which involves partial differential equations, has usually been less preferred over an approximate one with ODES, primarily to avoid computational complexities. However, an unprecedented growth in the computing power has made it possible to analyze dynamical systems more accurately with their more fundamental models involving PDEs. Interestingly, this approach has also opened up various fundamental system theoretic questions. For this causes the traditional finite dimensional state space to be substituted by an infinite dimensional one, which brings in its inherent issues to the domain of dynamical systems. In this talk, we shall address two such fundamental questions: stability and initial data. As we shall see in the talk, the answer to the question of stability comes by delving deep in the realm of functional analysis. On the other hand, the question of initial data shows promises of a satisfactory resolution with an approach involving commutative algebra and algebraic geometry.
Debasattam Pal received his Bachelor of Engineering (B.E.) degree from the Department of Electrical Engineering of Jadavpur University, Kolkata, in 2005. He received his M.Tech. and Ph.D. degrees from the Department of Electrical Engineering, IIT Bombay, in the years 2007 and 2012, respectively. He then worked as an Assistant Professor in IIT Guwahati from July, 2012 to May, 2014. After that, he joined IIT Bombay in June, 2014, as an Assistant Professor in the EE Department. His main area of research is systems and control theory. More specifically, his areas of interest are: multidimensional systems theory, algebraic analysis of systems, dissipative systems, optimal control and computational commutative algebra.