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