Arup Pal's homepage



My main area of interest is noncommutative geometry. One finds a rich interplay here between ideas and techniques from algebra and functional analysis on one hand and from geometry and topology on the other. And this interaction between different areas of mathematics is precisely the kind of thing that attracts me. Right now, I am trying to understand how quantum groups fit into Connes' formulation of NCG.

One other reason I am excited about noncommutative geometry is the following. For me one of the two fundamental questions that are driving our persuit of knowledge is: what is the nature of our universe? Of course, we never did and never will know the actual answer, we can only approximate it. At various stages of human civilization, depending upon the state of knowledge and the ability to observe things at the time, we have had different theories, or different models. The so-called Glashow-Salam-Weinberg standard model is one of the more successful models of modern physics. There are certain unpleasant or ad-hoc features of this model that are better explained if one adopts Connes' modified version of the standard model which assumes space-time is a noncommutative geometric space rather than a classical one (See week 83 of John Baez' "This week's find" column for more details). Thus if you can prove a good theorem in NCG, you will contribute to a better understanding of the universe!

This is Tuesday, October 17, 22:58:08 IST, 2006
Last modified: Wed July 5 11:27:38 IST 2006