What I've learnt

I am back to the position I was in sometime last semester, where I am beginning to doubt my abilities as a mathematician. Given that this is a passing phase (I hope!), I decided to make a list of some of the things I have learnt since I got back from India in June.

C* algebras :
- Semi-projectivity and its relation to Shape theory for C* algebras
- Asymptotic morphisms and Shape equivalence
- Bartle-Graves selection principle and its relation to asymptotic morphisms
- C* bundles and C(X)-algebras
- Dauns-Hoffman theorem about bundles over the primitive spectrum
- Dixmier-Douady's results on local triviality of bundles of compact operators
- Inductive limit representation of bundles of semiprojective algebras
- K-theory sheaf associated to a C* bundle over the unit interval
- UCT and Kunneth theorem and the usefulness of geometric/projective resolutions
- Brown-Douglas-Fillmore theorem
- Generalized homology theories for C* algebras
- Mod-p K-theory and associated invariants
- Construction of Hochschild/Cyclic homology
- Construction of the (non-commutative) Chern character
- Finally understood Stokes' theorem

Unrelated to C* algebras :
- Structure theorem for finitely generated modules
- Presentation of modules and canonical forms of matrices

Hopefully, reading this sometime in the future will help me feel better about myself :)

Birthing Blues

I turn 26 tomorrow. I feel like I should be excited, that there should be people jumping with joy at the thought that I am a year older, that there should be fireworks and various alcohol-induced escapades. Needless to say, none of that is happening. Funny thing is, I don't really want any of that. I don't particularly like being the centre of attention in any room of people, so being -the dude- for a whole 24 hours might cause some serious stress.

I do plan to go get a beer or two with some good friends. I had cake a day early. I am now listening to Pandora play me some Massive Attack and Pink Floyd. Things could be worse. I could be YOU!

The Walls

She put down the phone, and made sure it was safe in its cradle, before walking back into the living room, and up the staircase. She entered the room - the walls stared back at her.

The room was as it always had been - clothes strewn on the floor, a playstation in the corner connected to the television, showing some game she had never seen before. She smiled in the memory of when she tried playing Mario Bros. for the first time and was so good at it the she almost beat him - and of how mad he had been that he didn't speak to her for an hour!

She looked up, and saw the Flag. Its beauty framed against the wallpaper. And she remembered.

The bookshelf by the side were filled with Alaistair Mcleans, and Louis Lamour - all of them dog-eared from use. Those stories delighted him! - tales of exploration and adventure, of sailing to new lands and to discover unknown treasures - to fight the good fight!

The picture on the wall of him in full armour for a school play - and she remembered the reasons.

On the bedside, a framed picture of his father. The medals of honour shining bright in the sunlight streaming in through the windows. A picture of heroism and honour! But .. what was that look in his eyes?

A guitar at the foot of the bed - such a treat to listen to! He had real talent! The guitar, painted in shades of black and khaki, its strings taut, ready to play the most melodious music, or the most terrible, ungodly wailing noises that she was starting to hear.

And then it hit her - all the pain came flaring back - all the pent-up loneliness and bitterness, almost blinding ... this agony! The anger when he left, kept up inside in the face of his happiness and excitement. The feeling of impotence when those nice men in suits had convinced her that they were doing their best to find him. The raw rage at that spineless general who came back home leaving them on their own. Those bastards!

Dating Rocks

This is a rather interesting article by BBC - about the most recent attempt at dating Stonehenge. The pomp and show associated with this article has me wondering about its authenticity.

On the one hand, one cannot be too sure that the scientists are doing real science, and not just making up numbers that fit the popularly held belief - so that they might be able to get more funding for the project. Their academic careers probably depend on making this project work (the University they presumably work for has given them a sabbatical to work on the project, and would definitely not want to see them return empty handed.)

On the other hand, there is the question of the media's integrity as well! Anyone who has watched the flood of news channels these last few years will have realized that there is a lot of money to be made in the making News - clearly the way they make money is by sensationalizing an issue to the extent to which people would pay money to watch other shows (in this case, Time-Watch) on one of their sister channels - and in the process doubling their revenue off the story!

But the story has definitely caught my attention. The results do sound cool!

BBC NEWS | Science/Nature | Dig pinpoints Stonehenge origins

Until now, the consensus view for the date of the first stone circle was anywhere between 2600 BC and 2400 BC.

Strictly speaking, the result was rounded down to "between 2400 BC and 2200 BC" - but 2300BC is taken as the average. .....

"It's quite extraordinary that the date of the Amesbury Archer is identical with our new date for the bluestones of Stonehenge," said Professor Darvill.

"The date of Stonehenge had been blowing in the wind. But this anchors it. It helps us to be secure about the chronology of events.

Communication Breakdown

This last week has been a rather pleasant one - giving a talk to some friends on Thursday about a subject that's dear to me was very exciting and very liberating in itself. Have found myself a little under-used this semester because of the lack of teaching, but this talk gave me something to think about when my mind was bored. That kind of thing helps a lot!

This upcoming week is going to be similar - Need to plan a 2 hour presentation to my advisor and sundry classmates about what I've been working on these past few months - continuous fields of C* Algebras. It is going to be quite tough, especially because I don't know if I understand things well enough to explain it to anyone else! That takes a whole new level of knowledge, and I am just beginning to scratch the surface - Help!

But hopefully, enough work and I should feel comfortable enough to give the maiden presentation - building on it might be harder because of a complete lack of perspective (why AM I doing what I'm doing?!)

Oh well, time will tell ...

Reproach

Ahh .. the beast of insecurity raises its ugly head again!
Begone, Begone thou foul fiend!

Disconnect

Read Upamanyu Chatterjee's English, August this week for what is probably the 10th time. As before, I was struck by the deep melancholy of the protagonist stuck under all that humour and bravado. It is a great book, especially from the eyes of someone like me, who has grown up in India, speaking English with a Hindi accent, reading Oscar Wilde while listening to Rafi, and at the same time being completely out of touch with the realities of rural India.

Often have I wondered about my right to call myself Indian - agreed, much of who I am is because I have grown up there, eating Pav-Bhaji and chasing BEST buses while decked out in gum-boots in the pouring rain in Bombay. But my outlook on life is very heavily influenced by Western ideas - the idea of premarital sex does not pose any ethical dilemmas, the thought of living in an English-speaking country for the rest of my life does not leave me muttering to myself about my fate - so who the hell am I?

Ever since I landed in Madras in 2000, I have given this some serious thought. Fortunately, the struggle to learn Tamil and French simultaneously, coming to grips with guttural Tamil (in college) and refined English (at home) and many other things I went through during those years have together left me feeling rather good about myself! Most importantly, the interesting mix of people I have met in Bombay, RV, Madras, Mysore and finally here in America have left me with a rather malleable cultural perspective. I enjoy listening to different accents and trying to catch turns-of-phrase which are typical of a certain community. There is a perverse joy in looking at an obviously stoic Indian girl and wondering how good she would be in the sack.

Yes, This is the kind of thing I do in my free time - think about, and write about myself. I do need a life.

Happy Birthday!

This might just be the first time I have remembered in nearly a decade. Go me!

It now seems appropriate to post what is possibly my favourite poem -

Where the mind is without fear and the head held high
Where knowledge is free
Where the world has not been broken up into fragments by narrow domestic walls
Where words come out from the depth of truth
Where tireless striving stretches its arms towards perfection
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit
Where the mind is led forward by Thee into ever-widening thought and action
Into that heaven of freedom, my Father, let my country awake.

- Rabindranath Tagore

The future of interfaces

So while checking the usual tech news this morning, I came across a fabulous collection of pilot videos from Mozilla Labs on their futuristic concept of a web interface known as Aurora. Now although it seems like the desktop is far too cluttered in these videos, it is exciting to realize that one day, we might have a 3-d interface by which we access information - an interface where things can be grouped together on the desktop more visually and also moved around the desktop more intuitively.

This seems to lead back to this incredibly cool demo by Jeff Han of a multi-touch user interface which gives, in my opinion, the best possible way in which one could interact with a 2-dimensional device.

Now, the neat thing about these things is that the world now seems to be in a position to provide the computing capabilities to make full use of these technologies - for instance, there is D-Wave's Orion quantum computer which can recognize images and tell one from another by being able to harness immense amounts of visual data.

Plus, there is this Microsoft-promoted visualization tool called Photosynth, which is able to collate photographs from flickr, tag them with meta-information and club them together to give a panoramic view of the object/place in question.

All this might seem too much like science fiction, but with the rate at which technology is going forward, I wouldn't be surprised if we had something like Aurora in action in another 5 years.

Protection

Just reading The Fifth Elephant by Terry Pratchett - The book begins with the death of a man named Wally Sonky, who was stuffed into a barrel of molten rubber. You see, Mr. Sonky was known for making, among other things, little "wallies" - a rather life-threatening business in a city full of orthodox dwarfs who don't even allow their women to shave, let alone use a condom.

So it seems appropriate that I blog about something similar - an effort by the National Aids Control Organisation (NACO) in India to spread the use of these wallies among the traditionally backward (and hence vulnerable) social groups. They have gone about giving condoms to the women of a rural community north of Delhi, and have educated them as to its benefits. The male-dominated society has responded well, and seems willing to take these measure to prevent the spread of STDs and unplanned parenthood.

This, to me, is a big deal. I very strongly believe that, whether one uses it or not, the option to use a condom without any social stigma associated to it should be available to every living human being. Unfortunately, though, there are a great many places in the world where using a condom is considered a sin, and a prevention of natural (ie. god-given) functions of the human body. Of course, they don't stop to think about the economics of raising children, or, for that matter, getting Aids.


BBC NEWS | South Asia | Condoms help tackle Indian taboos

"We first began marketing the female condom primarily among sex workers three years ago," he says.

"We then decided to introduce this among rural women, since they are also a vulnerable group with little access to public health services.