The Mathematical Legacy of Jacques Tits

Article Type

Research Article

Publication Title

Resonance

Abstract

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.

First Page

1687

Last Page

1702

DOI

10.1007/s12045-022-1464-5

Publication Date

10-1-2022

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