I am
Anirbit. I have completed my 3 year BSc. Physics Hons. course at
.
1. My next
official affiliation.
I am joining the Physics PhD program at
TIFR (Tata
Institute of Fundamental Research). As per the results
announced I have been given the department I had asked for i.e
DTP
(Departmental of Theoretical Physics).
My classes there will begin from 22
nd July 2008.
Once I join TIFR I won't be able to access and update this web-page.
Hence if you want to know what I am upto after 22
nd July
2008 then the
only way to do so would be to send me an email to my gmail address and
in the reply I can send you my then official email id and the new
webpage address.
Henceforth kindly send all emails to my gmail id (as given at
the end of this page).
2. A conference
selection.
I have been selected as a part of the 25 member delegation from India
to represent India at the
58th
Meeting of Nobel Laureates at Lindau, Germany. The 25 members span
an age group of undergraduates (from institutes like IITKgp, IITM,
St.Stephens etc) , PhD students, research fellows and assistant
professors.
From 29th June to 4th July 2008 is the main program when Physics Nobel
Laureates will interact with the students and young researchers across
the world. After that through an arrangement between Department
of Science and Technology (DST),Govt. Of India and DFG (the German
equivalent of DST) we would be taken on a trip of the top research
institues in Germany like Max-Planck Institute, the institute at
Potsdam, Stuttgart etc.
Hence as a part of this program I will at Germany from 28th June to
13th July 2008.
3. Two projects.
I recently did 2 projects for my courses and I thought it is worth
sharing them here since I feel what I have done is only a small
beginning and these ideas of mine can be taken forward to some more
extent. So if you feel like it then go through the following
documents and if you think anything here interests you and that you can
take the ideas forward then contact me! (My contact email
addresses are given below)
{The program is extremely naive and has a lot of scope for improvement.
The program is not very stable but still I think it does some
basic amount of what would be ideally expected. The program is written
for Octave but it will probably also run on matlab}
a) A
computer programming project for geodesics in Schwarszchild Space-Time.
Explanation
The program
b) A thought experiment in fluid dynamics.
4. Two paintings.
Here are 2 paintings of mine which I thought are worth sharing here.
These were done about 5-6 years ago when I used to be a regular with my
paint-brushes and pallette. Since then I have produced no art works...I
don't know when or whether ever I will go back to the canvas.
a) An old pillar and a tree in water.
( with black ink
and metal tipped "crow quill" pen )
b) A face.
(with oil-paint )
5. Geometry
At the end, I now finally come to the central attraction
and pivot of my life, Geometry! The fascination began in class 3 when I
started playing with the compass. It has only been exponentially
increasing for the last 12 years and now it is becoming my
profession. What has been a happy escapade for me from the
rigmarole of life is probably going to become my life itself.
Some of the ideas in Geometry that I have been recently dabbling
with or got myself introduced to and ideas that have currently
captivated my imagination are :
a) How Field Theory shows that you cannot trisect an angle
with ruler and compass!
b) Theory of elliptic curves. It was just too exciting to
see that a torus can be thought of a zero-set of a polynomial in
complex projective spaces. The related ideas about the fundamental
domain of the modular group are also looking exciting.
c) That Eisntein-Hilbert action can be interpreted in
terms of giving representations of Characteristic Classes, (the Euler
Class to be precise)!
d) Off late I started thinking about the properties of
connections on Lie Groups and Riemannian Metrics on Lie Groups. Things
seem very exciting with 4 structures playing together i.e the Group,
the C-infinity manifold, the Connection and the Riemannian Metric.
Things like tangent bundle of any Lie Group is trivial and then to see
how if the Lie Group is connected, compact and non-trivial then it is
of genus 1. (Thats the good old Torus!)
Of course professional
mathematicians will say that the above things are pretty obvious and
trivial but for me it was sheer excitement like that of a child who
discovered a lost toy.
These lines of thought were showing me that the connection on a vector
bundle need not be the goal of a study (as sometimes typical Physics
appraoches make it seem) but can be used a crutch at times to get to
some topological truth which wasn't very obvious without the help
of this extra structure.
Like in Einstein's theory of Gravity after all the song and dance about
the metric and the curvature the main Action Function from which all
the other equations can be obtained turns out to be a topological
invariant i.e the Euler Character of the Space-Time!
These thoughts have been
leading me to some other questions like:
a) When is the
zero-set of a polynomial compact?
b) When is the zero-set of
a polynomial a Lie Group?
I have no idea about the answers to these questions but I plan to keep
thinking.
At this point I plan to take up detailed studies of the following
during the next few months:
a) Generalized Gauss-Bonnet Theorem and classification of
surfaces.
b) Geometry of Spinors and Twistors and how these form the
structure for Theory of Gauge Fields in Physics.
(this is my primary focus now)
c) More about Lie Groups (like how connections and Riemannian
Metrics behave on them), Galois Theory and Representation Theory.
d) Advanced topics in General Relativity from books like
those by S.W.Hawking and Ellis and the later chapters of the book by
R.M.Wald.
e) Hope to start building some basics towards taking
up a serious study of Algebraic Geometry.
6. A look
back at the 3 years in the CMI Physics Department.
Generally this is what I do........
The
regions of Theoretical Physics that I have been exploring can be
broadly classified as General Relativity, non-Abelian Gauge
Theory and Classical and Quantum
Field
Theories. I am keenly interested in the interplay of Geometry and
Physics. The
regions of Geometry that I have been pursuing can be broadly classified
as Projective Spaces and Fibre Bundle Geometry (
Differential and Riemannian Geometry ).
My first attraction with these subjects began with the theory of
Solitons and Monopoles and the role of Homotopy theory and theory of
Hopf Fibration in
them.
I had done some preliminary studies in General Relativity and
Quantum Field Theory during my 1st year of BSc. and then I did a
rigorous study of General Relativity and I am currently purusing
Quantum Field Theory.
I am very fascinated by the Eisntein-Hilbert Action and
I am trying to explore this exciting idea, especially its ramifications
in low dimensional gravity. Low dimension gravity seems to have
deep structures involved in it.
I plan to pursure a research in the
above regions of Physics and Mathematics. In this page I have been
updating about the seminars, talks and other technical activities in
my academic life. I have also put up various perspectives and
insights of mine in the field of physics and mathematics.
Alongside I have also put up certain aspects of
my non-academic pursuits too if someone finds that to be interesting!
