Well I am back, pretty soon this time. Sometimes incredible things happen in stuff that you absolutely deteste...well this would be too strong a statement to what I mean to refer to, however let me say what I am talking about...it's the game of Cricket.

As all of IISc was sleeping, a group of math students awoke to life and freedom, A moment comes, which comes but rarely in history, when we step out from the old to the new, when an age ends and when the soul of a Department, long suppressed, finds utterance...well this is what Pandit Jawaharlal Nehru would have said, had he seen our team play, today.

This posts will involve a lot of names, if you do not know them, don't worry, just build an analogy to your favorite team. To say the least, I reached the venue late, as usual. I had a valid reason this time. Yesterday, I fell off my bicycle under mysterious circumstances...if I try to recall properly I think I was day- dreaming whilst riding. In the course of the accident, I hit my head hard onto the road. Ever since I am trying to recall what I could have forgotten!!! Regarding the same, I had an appointment with the doctor today morning, and hence the delay justified!!!.

I reached exactly half way into the match. That's when we started batting. The opposite team had put up a monstrous score of 110 in 15 overs, so the "Math Geeks( or rather Gundas) " had to get to work as soon as possible. Our first wicket was the pair, Dheeraj and Ramiz, two very adept batsmen. They held fort for almost nine over, scoring 66 runs in partnership, Dheeraj seemed to have the extra lucky spark today, because, he had two consecutive drop catches, with the same guy...this fellow had a very big hand in our victory.

After Dheeraj was out(was caught right on the boundary), the game still seemed close at hand, in fact people in the audience had now developed this easy feeling 'we are winning'...especially when Tapan hit a six for the first ball he faced. It did not remain rosy for long, as in the same over Tapan was bowled out, then Sachin made his entry . Now things started getting a little messy, Ramiz was soon out and with him, all the experienced batsmen were on the bench. Now was the moment of truth, the onus was on the middle order, and this is why Sachin exists...not Tendulkar, but Sharma.

The scenario is as follows, we need 36 runs from 24 balls, we have about four wickets left...but not many balls. At this stage we should make mention of one of the stars in the team- Ravi Prakash, unfortunately he had a bad day. Due to some miscommunication between Sachin and him, he got himself run out. He left the field crying tantrums at Sachin. Now Sachin had a two fold responsibility in winning the game for us. One that he could then stay clear of Ravi's wrath, and secondly he was the last batsman known for batting!!!.

He did live up to the expectations. After Ravi, we had Prahllad on the field, but not for long. And then Arpan, who is primarily known for his deadly bowling.

One of Sachin's shot was stopped right at the boundary, there was some dispute with the decision...Well our very own self appointed 'Fourth umpire' i.e Avijit ran straight to the field and started clarifying to the fielder on how he was wrong and that we deserved a boundary, another instance of craziness!!!

Then it was Kaka's(lovingly called Santanu sometimes!!!) time to enter the bout. The game now was at 12 runs from 8 balls. And lo Sachin hits a six and a four out of the last two deliveries of the second last over. So we are down to 2 runs from 6 balls., and now Santanu(with love) is on strike. Well, this is one instance when things can get really crazy in cricket...you could either expect a six out of the last ball...or no runs of the entire last over!!!

The bowler bowls the first ball of the last over, and Santanu makes an attempt to hit a big one...no luck. Then the second ball, this time he tries to place the ball, but again in vain... the the third ball...and still the man can't make contact with the ball. Now the audience is getting jittery and superstitious, Samya gets a cigarette, and claims that this is the good luck charm...the women are busy praying...Rahul is thinking of a mathematical proof as to how we can not lose, Shubhamay was counting how much he would have to spend on the 'Juice treat' if we win, Suparna was busy in getting the audience in order, Shibu was busy in adjusting Diganto's balding, so that it could reflect light onto the bowler,and hence blind him, Ravi went off for a leak, ...and all hell broke loose. Everybody had Santanu's name on their lips (and I swear this name would have been a curse, if not for the positive outcome of the match), and then the fourth ball,and yo he manages to make contact with the ball, Sachin runs from the other end, Santanu runs, the fielder misses the wicket and they run for the winning run...and the crowd runs to them...Truly was a moment of ecstasy.

We won...we defeated a tough opponent...We are champions in our group!!!

We are just two games away from being champions...I have my fingers crossed...But deep within I know these guys have what it takes to attain the title...

Cheers to the Math Cricket Team!!!!

P.S- Thanks to the cheer-leading squad under the leadership of the Cheerful Suparna. In fact as the players were running between the wicket, Suparna was running between the score keeper and the audience..and hence was the score updating link!!!

## Sunday, March 21, 2010

## Tuesday, March 16, 2010

### A lecture, a conjecture and a problem...

Here I am, back after a not so hectic,but a busy week. Well good news first, my guides back from Canada, so that means a bonus to my reading.

Yesterday I attended a lecture on a the 'Fuglede's conjecture'. The statement of the conjecture by itself is pretty messy, but the underlying idea is beautiful.Actually I reached late,and missing the first few minutes was too dear for me. The reason was simple, every mathematical talk will begin with a definition, and if you have skipped that, you could as well skip the entire lecture. The speaker was Prof. Shobha Madan from IIT Kanpur.

Before saying anything more about the lecture let me mention something about the speaker. For one, she's a woman, and women in mathematics are very few- in fact those that exist are super-smart, talking from my experience. There was a rumour floating around that Shoba Madan had withdrawn her membership from the American Mathematical Society, because America attacked Iraq, in a lopsided battle. It is no longer a rumour though, as I found her letter to AMS regarding her resignation on the net,you can find it here- http://www.thehindu.com/fline/fl2009/stories/20030509006913000.htm

It is not that I support such boycott, yet her move is exemplary.

Getting to the lecture, my unpunctuality got me just a peripheral understanding of the topic. A lot of it was mathematical jargon, hower some ideas were good. There was mix of different branches of mathematics in her proofs, especially Functional Analysis, Algebra and good amount of Combinatorics.

Let me tell you the problem. You are given a bounded region D, and a certain shape T.You have to tell me if it is possible to tile (in the usual sense of tiling the floor or the roof) D using tiles of shape T.

Sounds pretty banal right. But thats not the case. I will not elaborate on this problem anymore however will give instances where one can apply these ideas. The Fuglede's Conjecture asserts that such a tiling always exists when the domain D is nice(in a certain mathematical sense- which you need not bother).

For example imagine a hexagonal room,can one tile this room with triangles? well seems obvious right. Cutting the floor along the diameter of the hexagon you see that just six equi-triangular tiles are sufficient. Note that here we made a choice in the type of triangle, so in a sense we have not answered the question in full generality. The heart of the problem is to check for the possibility of a tiling starting with an

This problem has been the impetus for many masons of the past,,and a matter of secrecy, about their successful tiling assignments. With ever changing designs it is imperative that one answers a question of this type, as it will go a long way in efficient resource management.

In mathematics such problems are also called 'Packing problems' , and solutions to these are of utmost importance, in theory and and practice.

Let me get a little rigorous, one can easily picture that it is not possible to tile a region using circles, because there will always exist a non-trivial gap between the tiles. Extending this idea, one can ask ' what kind of regular polygons will result in possible tiling' It seems intuitive(but need not necessarily be true) that there should be a bound on the number of sides of the polygon-this is because as the number of sides increases the boundary of the polygon attains the shape of a circle(convince yourself,its easy!), and we know that a circle cannot tile ( this idea is due to Sandeep Bhupati ,my senior at IISc), its cool right. One often uses such methods to prove stuff in mathematics.

As the talk progressed I grappled with the proofs, finally decided to lay back and relax. It is not worth breaking ones head on technical jargon.

The talk was nice, actually I liked the speaker, she had this healthy confidence and composure throughout. I like to attend talks by experts, their understanding of the subject galvanizes me with a positive attitude to research in particular and life in general!!!

Here is a small problem if you would like to work out-

You are given a 8x8 chess board with two diagonally opposite corners deleted(note that we now have only 62 squares). The question is that if you have dominoes which cover exactly two squares of the chess board at a time,then is it possible to cover the 62 squares using exactly 31 pieces of dominoes?Whatever the answer, you got to tell me why!!!

Yesterday I attended a lecture on a the 'Fuglede's conjecture'. The statement of the conjecture by itself is pretty messy, but the underlying idea is beautiful.Actually I reached late,and missing the first few minutes was too dear for me. The reason was simple, every mathematical talk will begin with a definition, and if you have skipped that, you could as well skip the entire lecture. The speaker was Prof. Shobha Madan from IIT Kanpur.

Before saying anything more about the lecture let me mention something about the speaker. For one, she's a woman, and women in mathematics are very few- in fact those that exist are super-smart, talking from my experience. There was a rumour floating around that Shoba Madan had withdrawn her membership from the American Mathematical Society, because America attacked Iraq, in a lopsided battle. It is no longer a rumour though, as I found her letter to AMS regarding her resignation on the net,you can find it here- http://www.thehindu.com/fline/fl2009/stories/20030509006913000.htm

It is not that I support such boycott, yet her move is exemplary.

Getting to the lecture, my unpunctuality got me just a peripheral understanding of the topic. A lot of it was mathematical jargon, hower some ideas were good. There was mix of different branches of mathematics in her proofs, especially Functional Analysis, Algebra and good amount of Combinatorics.

Let me tell you the problem. You are given a bounded region D, and a certain shape T.You have to tell me if it is possible to tile (in the usual sense of tiling the floor or the roof) D using tiles of shape T.

Sounds pretty banal right. But thats not the case. I will not elaborate on this problem anymore however will give instances where one can apply these ideas. The Fuglede's Conjecture asserts that such a tiling always exists when the domain D is nice(in a certain mathematical sense- which you need not bother).

For example imagine a hexagonal room,can one tile this room with triangles? well seems obvious right. Cutting the floor along the diameter of the hexagon you see that just six equi-triangular tiles are sufficient. Note that here we made a choice in the type of triangle, so in a sense we have not answered the question in full generality. The heart of the problem is to check for the possibility of a tiling starting with an

*arbitrary*triangle, which again is not true(relying on intuition). Then we need to classify all the possible triangles that fit the bill, and this step will put the problem to rest.This problem has been the impetus for many masons of the past,,and a matter of secrecy, about their successful tiling assignments. With ever changing designs it is imperative that one answers a question of this type, as it will go a long way in efficient resource management.

In mathematics such problems are also called 'Packing problems' , and solutions to these are of utmost importance, in theory and and practice.

Let me get a little rigorous, one can easily picture that it is not possible to tile a region using circles, because there will always exist a non-trivial gap between the tiles. Extending this idea, one can ask ' what kind of regular polygons will result in possible tiling' It seems intuitive(but need not necessarily be true) that there should be a bound on the number of sides of the polygon-this is because as the number of sides increases the boundary of the polygon attains the shape of a circle(convince yourself,its easy!), and we know that a circle cannot tile ( this idea is due to Sandeep Bhupati ,my senior at IISc), its cool right. One often uses such methods to prove stuff in mathematics.

As the talk progressed I grappled with the proofs, finally decided to lay back and relax. It is not worth breaking ones head on technical jargon.

The talk was nice, actually I liked the speaker, she had this healthy confidence and composure throughout. I like to attend talks by experts, their understanding of the subject galvanizes me with a positive attitude to research in particular and life in general!!!

Here is a small problem if you would like to work out-

You are given a 8x8 chess board with two diagonally opposite corners deleted(note that we now have only 62 squares). The question is that if you have dominoes which cover exactly two squares of the chess board at a time,then is it possible to cover the 62 squares using exactly 31 pieces of dominoes?Whatever the answer, you got to tell me why!!!

## Monday, March 8, 2010

### The ten comandments of modern research....

Well the title seems to put light to my blowhard attitude,you could justifiably ask 'who are you to role out commandments'...well,the last time such an act took place,was,on Mount Sinai,where God gave the ten commandments to Moses,so that he could tell them to the Israelite s,Moses told the commandments,but he wasn't God.. So let me reiterate that my role in this act is only of a scribe...these are God given commandments,you should convince yourself about this fact before reading anything further.

Now the next logical question is when and how did God tell me these commandments?This is a logical question,but useless at this point.Just to tell you that I am in the company of Gods,one of them is 'The God of Complex manifolds'-now do you know what that means?If 'no',then don't bother...I guess the title God should be just good enough.

Getting to the heart of the matter,Here they go...

1)Believe and convince yourself that Research is what you are meant to do,otherwise you are wasting your time and somebody else's money-both are assets which could well have less asinine applications.

2)Learn the key words in your field.It helps in ways more than one.

For example,you can use Google more effectively(unless you think you are the only moron working on your problem!!!).It also helps to switch mathematical conversations into ordinary ones ,for example imagine a group of people discussing 'The invertiblity of the Fourier transform on Hilbert spaces over the field of Complex numbers' and you happen to barge in.Instead of having any knowledge of the Theorem as whole,its just enough to know about the key words in this statement,like,who cares what the Fourier transform is,I know who Fourier is(He is a great mathematician for one)!!!and if you are eloquent enough,you could even shift the focus from the 'Fourier transform ' to 'Fourier 'himself!

3)Remember 'Confusion' rules the world.If you cannot convince,try to confuse.It improves the perplexity of your statements.

By the way,in the past, Mathematics that was conceivable by the common man was considered to be an object of triviality.

4)Learn your topic in such a way that you can enlighten the common man and befuddle the expert.

5)Just because you have the 'researcher' tag...do not assume that people who don't have it are fools.They do research in topics which do not need a tag.Basically be humble and kind to people who do not know how to differentiate and integrate!!!

6)Besides doing purely abstract research,spend time in doing something that might have a more immediate application.It feels good sometimes to know that people actually use what you have found!!!

7)Treat your theorems like 'Chicken Jokes'.You see someone asked 'why did the chicken cross the road?' and lo- behold there was this revolution of jokes!!!Anyways wat I mean to say is that,most of the theorems came into being because of similar questions,in fact even sillier ones like'In how many ways can the chicken cross the road' or rather 'If the chicken takes too long to cross,then, will it still remain a chicken'...and so on.

8)Do not hesitate to ask trivial questions.

If you analyze,you will realize that most of the theorems are built using simple blocks.Newton says that he could do so much because the sat on the shoulders of giants.In fact as Hardy says in his book 'A mathematicians apology' that the most exemplary proof is the simple proof of the infinitude of primes.

9)Learn to work hard smartly.

10)Remember that the most valuable resource that you have is your time,use it wisely.

So do not waste too much time now,if you haven't already wasted the last 15 minutes...and get back to something more constructive...

Now the next logical question is when and how did God tell me these commandments?This is a logical question,but useless at this point.Just to tell you that I am in the company of Gods,one of them is 'The God of Complex manifolds'-now do you know what that means?If 'no',then don't bother...I guess the title God should be just good enough.

Getting to the heart of the matter,Here they go...

1)Believe and convince yourself that Research is what you are meant to do,otherwise you are wasting your time and somebody else's money-both are assets which could well have less asinine applications.

2)Learn the key words in your field.It helps in ways more than one.

For example,you can use Google more effectively(unless you think you are the only moron working on your problem!!!).It also helps to switch mathematical conversations into ordinary ones ,for example imagine a group of people discussing 'The invertiblity of the Fourier transform on Hilbert spaces over the field of Complex numbers' and you happen to barge in.Instead of having any knowledge of the Theorem as whole,its just enough to know about the key words in this statement,like,who cares what the Fourier transform is,I know who Fourier is(He is a great mathematician for one)!!!and if you are eloquent enough,you could even shift the focus from the 'Fourier transform ' to 'Fourier 'himself!

3)Remember 'Confusion' rules the world.If you cannot convince,try to confuse.It improves the perplexity of your statements.

By the way,in the past, Mathematics that was conceivable by the common man was considered to be an object of triviality.

4)Learn your topic in such a way that you can enlighten the common man and befuddle the expert.

5)Just because you have the 'researcher' tag...do not assume that people who don't have it are fools.They do research in topics which do not need a tag.Basically be humble and kind to people who do not know how to differentiate and integrate!!!

6)Besides doing purely abstract research,spend time in doing something that might have a more immediate application.It feels good sometimes to know that people actually use what you have found!!!

7)Treat your theorems like 'Chicken Jokes'.You see someone asked 'why did the chicken cross the road?' and lo- behold there was this revolution of jokes!!!Anyways wat I mean to say is that,most of the theorems came into being because of similar questions,in fact even sillier ones like'In how many ways can the chicken cross the road' or rather 'If the chicken takes too long to cross,then, will it still remain a chicken'...and so on.

8)Do not hesitate to ask trivial questions.

If you analyze,you will realize that most of the theorems are built using simple blocks.Newton says that he could do so much because the sat on the shoulders of giants.In fact as Hardy says in his book 'A mathematicians apology' that the most exemplary proof is the simple proof of the infinitude of primes.

9)Learn to work hard smartly.

10)Remember that the most valuable resource that you have is your time,use it wisely.

So do not waste too much time now,if you haven't already wasted the last 15 minutes...and get back to something more constructive...

## Wednesday, March 3, 2010

### Rangoli Holi et al...

Well on 1st March we celebrated Holi,was a different experience I should say.When in Goa we only celebrate the traditional Carnival,with pomp and gaiety(thats how the slogan goes)...if you have been to Goa you would know what I mean.The Carnival is a pagan celebration,which gets along with it a lot of vices,which if one avoids,its a pleasant experience.

Just a little digression,the previous day,the Hindi Samiti at IISc organized 'Rangoli competition'.I always thought it was a simple task to put powder on the floor in such a way that it represents some familiar design,wasn't the case.However our motives for participating were not so noble towards creativity ...the truth was that a friend of my friend told my friend that there was just one participant enrolled,and hence if we reached the venue on time at least, the 2nd prize was assured.So we decided to team up,and rush to the venue,on the way we happily discussed the posibility of winning the first prize(since the 2nd was already in our kitty!!!).The scene was different at the venue,this guy had told so many people about the scarcity in participants that,everybody rushed to compete for the 2nd prize.They would not even let us participate.We finally got a chance to try our hands at it.The theme of our Rangoli was 'Reaserch at IISc',as you can see in the picture-it was 'music+coffee+nature=proofs of theorems'.We got a consolation prize,which was good enough,as compared to the 2nd prize.We were pretty pleased with our efforts,though they might not have got us the best results.Its fun to work as a team,and create something close to modern abstract art.As the prizes were bieng distributed,we were told that,having 'Rangoli' at ones doorstep,helps eclipse negative energies.And in general adds color to the household.It was a great experience,even though the 2nd prize was a disappointment.

Getting back to Holi at IISc,as I said before it was my first experience...and it was awesome,except for the fact that those jerks used dye to color people.Had to almost scrape my skin off to get rid of the color.

The fun began after lunch,was told that there was holi activity going on at the mess...I managed to get myself safely into the mess,with not a drop of color on me,I felt an air of jubilation at fact that I managed to get away from those 'coloring guys',however I could not manage to keep on to it for long.

That afternoon I was supposed to meet my guide(each student has to work under a Prof,whom they call 'guide' or 'boss' outside private circles!!!),my meeting wasn't scheduled though,however was planning to tell him after lunch.As I was leaving the mess,there came this guy running after me,was pretty obvious what plans he had for me...so I started running too(This is one instant where jogging regularly helps!!!),I outran him,but then thought it was poor spirit to behave like this on a festive occasion like this,so I stopped waited for him and then told him politely why he should not color me...luckily the man had a heart(besides brains!!!),he believed me,and just to make up for the energy he spent in chasing me,wished me with his colored hands.So far so good.I go a little far,and then there comes another fellow,this one turned out to be a rascal...put color on me without any warning.Now I had some soul searching to do,I had two desires within me,one to chicken out,just wash my face and go and meet my guide,this did not seem exciting,the other more manly and gallant was to stay on and have my own victims of color!!!which I did!!!At the end my face was colored beyond recognition....we looked like creatures from Pandoras.I left midway(after satisfying myself that I had accomplished what I stayed back for),went to my room immediately,and scrubbed my face for 30 odd minutes to get the dye off me.

Then went and met my guide...and hence got both my desires fulfilled.

In all it was a wonderful experience.It is supposed to be The festival of colors.We sometimes get so lost in our daily chores,that we hardly realize how colorful life is,and occasions like these remind you about this fact.The energy you see in people who celebrate is awesome,its great fun.

If you missed it this time...don't worry,in the coming year bond with people who celebrate and you too can have a great time...a great time it is!

Just a little digression,the previous day,the Hindi Samiti at IISc organized 'Rangoli competition'.I always thought it was a simple task to put powder on the floor in such a way that it represents some familiar design,wasn't the case.However our motives for participating were not so noble towards creativity ...the truth was that a friend of my friend told my friend that there was just one participant enrolled,and hence if we reached the venue on time at least, the 2nd prize was assured.So we decided to team up,and rush to the venue,on the way we happily discussed the posibility of winning the first prize(since the 2nd was already in our kitty!!!).The scene was different at the venue,this guy had told so many people about the scarcity in participants that,everybody rushed to compete for the 2nd prize.They would not even let us participate.We finally got a chance to try our hands at it.The theme of our Rangoli was 'Reaserch at IISc',as you can see in the picture-it was 'music+coffee+nature=proofs of theorems'.We got a consolation prize,which was good enough,as compared to the 2nd prize.We were pretty pleased with our efforts,though they might not have got us the best results.Its fun to work as a team,and create something close to modern abstract art.As the prizes were bieng distributed,we were told that,having 'Rangoli' at ones doorstep,helps eclipse negative energies.And in general adds color to the household.It was a great experience,even though the 2nd prize was a disappointment.

Getting back to Holi at IISc,as I said before it was my first experience...and it was awesome,except for the fact that those jerks used dye to color people.Had to almost scrape my skin off to get rid of the color.

The fun began after lunch,was told that there was holi activity going on at the mess...I managed to get myself safely into the mess,with not a drop of color on me,I felt an air of jubilation at fact that I managed to get away from those 'coloring guys',however I could not manage to keep on to it for long.

That afternoon I was supposed to meet my guide(each student has to work under a Prof,whom they call 'guide' or 'boss' outside private circles!!!),my meeting wasn't scheduled though,however was planning to tell him after lunch.As I was leaving the mess,there came this guy running after me,was pretty obvious what plans he had for me...so I started running too(This is one instant where jogging regularly helps!!!),I outran him,but then thought it was poor spirit to behave like this on a festive occasion like this,so I stopped waited for him and then told him politely why he should not color me...luckily the man had a heart(besides brains!!!),he believed me,and just to make up for the energy he spent in chasing me,wished me with his colored hands.So far so good.I go a little far,and then there comes another fellow,this one turned out to be a rascal...put color on me without any warning.Now I had some soul searching to do,I had two desires within me,one to chicken out,just wash my face and go and meet my guide,this did not seem exciting,the other more manly and gallant was to stay on and have my own victims of color!!!which I did!!!At the end my face was colored beyond recognition....we looked like creatures from Pandoras.I left midway(after satisfying myself that I had accomplished what I stayed back for),went to my room immediately,and scrubbed my face for 30 odd minutes to get the dye off me.

Then went and met my guide...and hence got both my desires fulfilled.

In all it was a wonderful experience.It is supposed to be The festival of colors.We sometimes get so lost in our daily chores,that we hardly realize how colorful life is,and occasions like these remind you about this fact.The energy you see in people who celebrate is awesome,its great fun.

If you missed it this time...don't worry,in the coming year bond with people who celebrate and you too can have a great time...a great time it is!

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