The Large Hadron Collider, working on the Swiss-French border for identifying the “god particle (the Higgs-boson),” is considered the biggest experiment in human history to solve the origin of the universe. No less significant are the experiments to decode the DNA and the mysteries of the human genome in the field of biological sciences.
The scope for such large experiments in mathematics, according to International Mathematical Union president L. Lovasz, is, however, limited. “The scope of Mathematics is so broad that it cannot be compressed. There are important problems and they need important directions,” he said.
Mr. Lovasz introduced winners of four Field Medals (considered the Nobel equivalents), the Rolf Nevanlinna prize, Carl Friedrich Guass prize for applied mathematics and the Chern Medal award, the award being presented for the first time at the International Congress of Mathematicians (ICM)-2010 that got off here on Thursday.
Elon Lindenstrauss of the Hebrew University of Jerusalem, Ngo Bao Chau, Universite Paris-Sud, Orsay, France Stanislav Smirnov of Universite De Geneve, Switzerland and Cedric Villani of Institut Henri Poincare, Paris, France were selected for the Fields Medal award during the current edition of the ICM. The Fields Medal is presented to those below 40 to recognise outstanding mathematical achievements for existing work and for the promise of future achievements.
Mr. Lindenstrauss made far-reaching advances in ergodic theory, the study of measure preserving transformations. His work on a conjecture of Furstenberg and Margulis concerning the measure rigidity of higher rank diagonal actions in homogenous spaces led to striking applications.
Given the award for his proof of the fundamental Lemma in the theory of automorphic forms through introduction of new algebra-geometric methods, Ngo's achievement which lies at crossroads between algebraic geometry, group theory and automorphic forms is leading to many striking advances in the Langlands programme as well as the subjects linked to it.
Mr. Smirnov made outstanding contributions to prove the scaling limit of various two dimensional models in statistical physics has an unexpected symmetry. His work gave solid foundation for important methods in statistical physics like Cardy's Formula. Mr. Cedric Villani, who worked on nonlinear Landau damping and convergence to equilibrium for Boltzmann equation, is one of the pioneers in application of optimal transport theory to geometric and functional inequalities.
Daniel Spielman of Yale University was chosen for Rolf Nevanlinna prize for “smoothed analysis of linear programming, algorithms for graph-based codes and applications of graph theory to numerical computing” and made remarkable contributions to the field of Simplex Method.
Yves Meyer, professor emeritus at Ecole Normale Superieure de Cachan, France, has been selected for the prestigious 2010 Guass prize for his fundamental contributions to number theory, operator theory and harmonic analysis and his pivotal role in the development of wavelets and multi-resolution analysis.
Louis Nirenberg of the Courant Institute of Mathematical Sciences, New York University, has become the first recipient of the Chern medal, established in the memory of Chinese mathematician Shiing-Shen Chern. Acclaimed as one of most outstanding analysts and geometers of the century, Mr. Nirenberg had a major influence in the development of several areas of mathematics and their applications.