|Overview||Bhaskaracharya Pratishthana is organising a Symposium in Mathematics for Mathematics students and teachers on the occasion of the Birth Day of Founder Director Professor Shreeram S. Abhyankar, a world famous Mathematician. Prof. Abhyankar was born on 22nd July 1930 in Ujjain.|
|Date||Saturday, 22nd July 2017|
|1||Prof. Balwant Singh||Centre for Basic Sciences, Mumbai|
|2||Prof. R. V. Gurjar||IIT Bombay|
|3||Prof. S. M. Bhatwadekar||Bhaskaracharya Pratishthana|
|Prof. Balwant Singh||The Jacobian Conjecture||
The Jacoboian Conjecture in dimension two states that if f = f (X, Y ) and g = g(X, Y ) are polynomials in two variables X and Y with real coefficients (or cofficients in any field k of characteristic zero) such that their Jacobian
There is a similar conjecture in dimension n.
The conjecture was formulated in 1939, and it is still open even for n = 2. The efforts of several mathematicians over the past decades have yielded only partial results.
We shall describe some of these partial results.
|Prof. R. V. Gurjar||Singularities|| In this lecture we will discuss how singular points occur naturally when dealing with zeros of polynomials. We will look at some powerful tools developed by mathematicians to study them. Several beautiful results proved using these methods will be mentioned.
|Prof. S. M. Bhatwadekar||Epimorphism problems in Affine Geometry||
One of most significant contributions of (late) Professor Shriram Abhyankar is the following famous Abhyankar-Moh/Suzuki Epimorphism Theorem:
Theorem. Let k be a field of characteristic zero. Let F ∈ k[X, Y ] be such that .k[X, Y ]/(F ) ≈ k[T ]. Then F is a variable in k[X, Y ] i.e. ∃ G ∈ k[X, Y ] such that k[X, Y ] = k[F, G].
This result led to many important questions in affine geometry. To cite one (known as Abhyankar-Sathaye Epimorhism Problem):
k[X1 , X2 , · · · , Xn ] = k[F1, · · · , Fn−m, G1 , · · · , Gm]?
|1||Please click here for the registration form|
|2||List of selected participants will be announced later|