One of the important contributions made by Fields Medal winner Manjul Bhargava is the generalisation of the ‘composition law’ of binary quadratics (polynomial expressions of the form ax2 + bxy + cy2) discovered 200 years ago by Carl Friedrich Gauss (1777-1855), to higher degree polynomials using an ingenious geometric technique that he discovered.
The awards were announced at the inaugural of the nine-day International Congress of Mathematicians that began in Seoul on Wednesday.
The awards, presented at the quadrennial ICM event, include the Fields Medal, the highest award in mathematics; the Rolf Nevanlinna Prize and the Carl Friedrich Gauss Prize. At the last ICM held in Hyderabad, the Chern Medal and the Leelavati Prize were added.
The Fields Medal is awarded “to recognise outstanding mathematical achievement for existing work and for the promise of future achievement”. “Manjul Bhargava has developed powerful new methods in the geometry of numbers and applied them to count rings of small rank and to bound the average rank of elliptic curves,” said the medal citation.
Besides mathematics, Dr. Bhargava pursues his interests in linguistics and Indian classical music. The Indian-American theoretical computer scientist Subhash Khot, a theoretical computer scientist at the Courant Institute of Mathematical Sciences of New York University, gets the Rolf Nevanlinna Prize. The citation for him read: “Subhash Khot’s prescient definition of the Unique Games problem, and his leadership in the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimization problems, have produced breakthroughs in algorithmic design and approximation hardness, and new exciting interactions between computational complexity, analysis and geometry.”
Born in Ichalkaranji in Maharashtra, Dr. Khot (36) an IIT Bombay alumnus, won the silver medal in the International Mathematics Olympiad in 1994 and 1995 and stood first in the IIT Joint Entrance Examination in 1995. His area of research is Computational Complexity Theory. His Unique Games Conjecture is about the impossibility of even obtaining good approximations to problems that are computationally hard to solve using standard computing algorithms.
