Its almost the end of the year and i dont know what i have really gained in these holidays or perhaps, lost. I am currently attending this workshop on Classical groups and it has been a nightmare. I enter the class on the very first day of the conference and am really un-intimidated by the style of people, anupam reading Sury'
s limerick which was kinda funny,the way Anupam said it, director giving a nice intro to the conf. folks and the most funny part in his speech was something like the following. :" i know you are mathematics people,theoretical people, but come visit our labs". and i could not stop grinning like a kid who knows what the other naughty kid is upto. well then the conference started with introductory lecture of Shripad of which i did not make out anything, later anupam started with basic group theory concepts and whatever we had learnt in an entire course in group theory,anupam summarised in 5 minutes and then the fun part started. We know the definition of a group action and obiously as though emphasised by Chandrasheel, it is more important that it looks like,group action is used like all the time. coming back to the topic,we know what a transitive action is, action which has only one orbit. now comes the stuff i learnt or so i think. we define something called a doubly transitive action in which a pair of set elements go to some other pair of set elements by the action of some group element. this is a stronger version of transitivity and hell it is more important than it seems. now comes the concept of a block(B) in the set on which the group is acting, it is a proper subset which satisifies a property that any group element acting on the subset B leaves it invariant setwise or creates a new subset which is disjoint from B. Now if a group acts on a set such that there are no blocks then the action is called primitive. And primitivity is an important notion. The only connection between doubly transitive action and primitivity is that if the action is doubly transitive then it is primitive, this can be proved easily. Later comes the core theorem called Iwasawa theorem which is basically a machinary to prove that some group is simple. Why should we care whether a group is simple or not. we will come to that question later. What exactly does Iwasawa theorem state. it states that if the group action is transitive and primitive and that there is a normal subgroup in the stabilizer of some set element such that the ......then the group is simple. pardon me. well later in the book which we are following or rather stopped following is Larry Grove's 'Classical groups and Geometric algebra'. the idea is simply to find simple groups. and we find new simple groups which i had never seen before.groups which are created by going into projective geometry and then groups which are isometries over an alternate bilinear form or a symmetric one,with some modification to the group. i stopped understanding since the beggining of this week.we had some fantastic mathematicians coming and giving a talk like George Lutszig and MS ragunathan today who had met and had several correspondence with the great mathematician Andre Weil(who literally started calling some groups as classical groups and the terminology stuck) and Grothendieck himself. Some important person are yet to come. I think i will stop visiting the workshop coz i dont understand anything these days,today in raghunathan's lecture i was studying the ring theory from artin. and i dont seem to making any progress,as always. hermann weyl was a colorful character as raghunathan was recouting from his meeting with weyl in tifr in 60s. i think i want to be a mathematician. the only subject where i see theoreitcal buildup,whatever that means, is in mathematics. they define objects abstractly,they deduce somethings,they make more structure, they deduce some more, just to fit the picture,they bend the structures,they twist 'em and later remove the entire pile. several such instances and you get a good definition and then you work on it. i have not seen this in any other subject and i love it. well sometimes i hate it too.
well apart from the conference, i wasted my entire december. i should have learnt or at least revised linear algebra,done some group theory problems, done some analysis.lately i have started running from my hostel to puc and back. i have been consistent about it in december except maybe for 3 days. i hope to continue it but considering my lack of willpower i really dont know.
i completed Boardwalk empire,all 4 seasons and also Breaking bad,all 5 seasons. liked both of them.
this december i was supposed to attend this movie making workshop being held here but i joined the classical groups camp and i can't do movie making and yet i do not regret but i would have been little less sad if i could do both.
s limerick which was kinda funny,the way Anupam said it, director giving a nice intro to the conf. folks and the most funny part in his speech was something like the following. :" i know you are mathematics people,theoretical people, but come visit our labs". and i could not stop grinning like a kid who knows what the other naughty kid is upto. well then the conference started with introductory lecture of Shripad of which i did not make out anything, later anupam started with basic group theory concepts and whatever we had learnt in an entire course in group theory,anupam summarised in 5 minutes and then the fun part started. We know the definition of a group action and obiously as though emphasised by Chandrasheel, it is more important that it looks like,group action is used like all the time. coming back to the topic,we know what a transitive action is, action which has only one orbit. now comes the stuff i learnt or so i think. we define something called a doubly transitive action in which a pair of set elements go to some other pair of set elements by the action of some group element. this is a stronger version of transitivity and hell it is more important than it seems. now comes the concept of a block(B) in the set on which the group is acting, it is a proper subset which satisifies a property that any group element acting on the subset B leaves it invariant setwise or creates a new subset which is disjoint from B. Now if a group acts on a set such that there are no blocks then the action is called primitive. And primitivity is an important notion. The only connection between doubly transitive action and primitivity is that if the action is doubly transitive then it is primitive, this can be proved easily. Later comes the core theorem called Iwasawa theorem which is basically a machinary to prove that some group is simple. Why should we care whether a group is simple or not. we will come to that question later. What exactly does Iwasawa theorem state. it states that if the group action is transitive and primitive and that there is a normal subgroup in the stabilizer of some set element such that the ......then the group is simple. pardon me. well later in the book which we are following or rather stopped following is Larry Grove's 'Classical groups and Geometric algebra'. the idea is simply to find simple groups. and we find new simple groups which i had never seen before.groups which are created by going into projective geometry and then groups which are isometries over an alternate bilinear form or a symmetric one,with some modification to the group. i stopped understanding since the beggining of this week.we had some fantastic mathematicians coming and giving a talk like George Lutszig and MS ragunathan today who had met and had several correspondence with the great mathematician Andre Weil(who literally started calling some groups as classical groups and the terminology stuck) and Grothendieck himself. Some important person are yet to come. I think i will stop visiting the workshop coz i dont understand anything these days,today in raghunathan's lecture i was studying the ring theory from artin. and i dont seem to making any progress,as always. hermann weyl was a colorful character as raghunathan was recouting from his meeting with weyl in tifr in 60s. i think i want to be a mathematician. the only subject where i see theoreitcal buildup,whatever that means, is in mathematics. they define objects abstractly,they deduce somethings,they make more structure, they deduce some more, just to fit the picture,they bend the structures,they twist 'em and later remove the entire pile. several such instances and you get a good definition and then you work on it. i have not seen this in any other subject and i love it. well sometimes i hate it too.
well apart from the conference, i wasted my entire december. i should have learnt or at least revised linear algebra,done some group theory problems, done some analysis.lately i have started running from my hostel to puc and back. i have been consistent about it in december except maybe for 3 days. i hope to continue it but considering my lack of willpower i really dont know.
i completed Boardwalk empire,all 4 seasons and also Breaking bad,all 5 seasons. liked both of them.
this december i was supposed to attend this movie making workshop being held here but i joined the classical groups camp and i can't do movie making and yet i do not regret but i would have been little less sad if i could do both.
