• Sury B

      Articles written in Resonance – Journal of Science Education

    • On Some of Jean Bourgain’sWork∗

      Sury B Kaushal Verma

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      The Belgian mathematician Jean Bourgain was born in Ostendein 1954. After a whirlwind career during which hesolved many deep problems and transformed several areas ofmathematics, he passed away in Bonheiden on 22nd December2018 (the birth anniversary of Ramanujan). Bourgainwas the modern-day equivalent of Leonhard Euler, makingprolific contributions to a wide variety of problems in mathematicsand physics. The Mathematical Reviews cite 511 publicationsunder his name. Such a wide spectrum of work cannotbe described in one article with any justice even if theauthors were to possess expertise in a number of these areas.The breadth and depth of Bourgain’s work can be fathomedfrom the following phrase used in a review by a renownedmathematician Ben Joseph Green; he said, “It is beyond thecapability of the reviewer to give anything like a meaningfuldescription of the argument here, save to repeat the authors’comments....” The review was of a paper that completelysolved Vinogradov’s mean value conjecture in analyticnumber theory. We choose a small assortment of the topics towhich he contributed so deeply and, describe some technicaldetails in rough terms. In the end, we make a brief mention ofhis results in a wide variety of areas (see [3–5], [7–14] for technicaldetails). The topics we dwell on in this write-up includethe so-called Kakeya problem and some striking applicationsto number theory.

    • ICM Awards 2018

      Sury B

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      The International Congress of Mathematicians (ICM) met inBrazil in August 2018 for its quadrennial conference. Duringthe ICM, the Fields Medals and some other awards are presented.In this report, we briefly recount the personages andthe significance of their work.

    • Veeravalli S Varadarajan: 18th May 1937 – 27th April 2019

      Sury B

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    • Smooth Jordan Curves Inscribe Every Rectangular Shape

      Sury B

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    • John Horton Conway: The Magical Genius Who Loved Games

      Arvind Ayyer Sury B

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    • The Mathematical Legacy of Jacques Tits

      Sury B

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      The 'Erlangen Program' of Felix Klein worked by 'reduc­ing' problems in geometry to the study of their symmetry groups-thereby algebraizing geometry. Jacques Tits's work goes in the opposite direction-he made fundamental contri­butions to the abstract theory of groups via geometric meth­ods. His geometric techniques apply to not only finite groups, but also to rather diverse situations such as groups defined over the $p$-adic numbers, and to the so-called arithmetic groups etc. Tits's ideas have enriched many of the important ad­vances in group theory and geometry in the last six decades. He designed the theory of so-called 'buildings' which incor­porates geometrically the algebraic structure of linear groups. Amazingly, these ideas have also led to applications in sub­jects like the study of Riemannian manifolds of higher rank that are seemingly remote from the original developments.

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