Photographs from the workshop

Here are three photographs from the recent instructional school in IMSc, Chennai:

1. JK talking about KK scaled original
2. animated discussion between Partha and Sunder scaled original
3. group photo on the last day scaled original

K-theory notes

Here is the pdf file of the notes that I have prepared while giving a course on K-theory recently during a workshop on NCG in IMSc, Chennai. I have used the books by Wegge-Olsen and Higson/Roe (Analytic K-homology) and the notes by Matthes/Szymanski on the topic.

Papers on quantum spheres

Here are two papers that I have uploaded to the arxiv recently:

Characterization of $SU_q(\ell+1)$-equivariant spectral triples for the odd dimensional quantum spheres

Authors: Partha Sarathi Chakraborty, Arupkumar Pal
Comments: LaTeX2e, 20 pages
Subj-class: Quantum Algebra; K-Theory and Homology; Operator Algebras
MSC-class: 58B34, 46L87, 19K33

The quantum group has a canonical action on the odd dimensional sphere . All odd spectral triples acting on the space of and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial -homology class. These generalize the results of Chakraborty & Pal for .

Source: http://arxiv.org/abs/math.QA/0701694

Torus equivariant spectral triples for odd dimensional quantum spheres coming from $C^*$-extensions

Authors: Partha Sarathi Chakraborty, Arupkumar Pal
Comments: LaTeX2e, 12 pages
Subj-class: K-Theory and Homology; Operator Algebras; Quantum Algebra
MSC-class: 58B34, 46L87, 19K33

The torus group has a canonical action on the odd dimensional sphere . We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial -homology class thus generalizing our earlier results for . We also relate the triple we construct with the -extension .

Source: http://arxiv.org/abs/math.KT/0701738

Moving house

I will slowly move most of the material in my present homepage to this page, because it is so much easier to add/modify material here, and I dont have to worry about the design etc. Downloadable material will still be hosted there, but the links will be available here.

Some of my favourite links

• John Baez‘s home page. I would specially recommend “this week’s finds in mathematical physics“.

• arxiv.org a very very useful site. If you are a mathematician and do not submit your papers here, please consider doing so in future — your papers will be read by more people, and more importantly, by those who can not afford to buy expensive journals.

• www.mathpages.com, can keep you absorbed for hours.

• Biographies of mathematicians, past and present.

• this page will give you some idea as to what a good thesis problem should be like

• James S. Milne, try his “tips for authors“

• Have you heard of Perceived Depth Images? Visit this page if you have not.

• NASA image gallery, archives thousands of breathtaking images, taken from various space ships. If your interest in human space missions goes beyond these images, here is a good point to start.

• My photo album at fotopic.net.