1987 - Member of the National Academy of Sciences
1978 - Brouwer Medal
His primary areas of study are Algebra, Humanities, Pure mathematics, Group theory and Algebraic geometry. Many of his research projects under Algebra are closely connected to Elementary arithmetic with Elementary arithmetic, tying the diverse disciplines of science together. His study on Characteristic class is often connected to Homogeneous as part of broader study in Pure mathematics.
His biological study spans a wide range of topics, including Algebraic cycle, Function field of an algebraic variety, Representation theory and Real algebraic geometry. His work carried out in the field of Real algebraic geometry brings together such families of science as Algebraic surface, Reductive group, Borel subgroup and Dimension of an algebraic variety. The concepts of his Algebraic geometry study are interwoven with issues in Arithmetic function and Automorphic form.
Armand Borel spends much of his time researching Pure mathematics, Algebra, Lie group, Group theory and Simple Lie group. His work in Pure mathematics is not limited to one particular discipline; it also encompasses Topology. His Algebra research incorporates elements of Number theory and Algebra over a field.
Armand Borel interconnects Algebraic cycle and Representation theory in the investigation of issues within Group theory. His Simple Lie group study incorporates themes from Representation of a Lie group, Maximal torus and Killing form. His research in Group of Lie type intersects with topics in E8 and Algebraic group.
Armand Borel mainly focuses on Pure mathematics, Algebra, Lie group, Simple Lie group and Automorphic form. He connects Algebra with Local zeta-function in his research. The study incorporates disciplines such as Conjugacy class and Fundamental group in addition to Lie group.
Armand Borel has included themes like Real form, Representation theory, Lie theory and Killing form in his Simple Lie group study. His work deals with themes such as Group theory and Group of Lie type, which intersect with Representation theory. The Automorphic form study which covers Poincaré series that intersects with Cusp form.
Armand Borel mainly investigates Pure mathematics, Mathematical analysis, Triple system, Lie group and Symmetric space. His Mathematical analysis research includes themes of Automorphism, Combinatorics, Torus, Bibliography and Invariant. His Triple system study also includes fields such as
Armand Borel combines subjects such as Freudenthal magic square, Killing form, Group theory, Reductive group and Real form with his study of Representation theory. His Freudenthal magic square research is classified as research in Algebra. With his scientific publications, his incorporates both Algebra and Mayer–Vietoris sequence.
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Linear algebraic groups
Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups
Armand Borel;Nolan R. Wallach.
Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts
Annals of Mathematics (1953)
CHARACTERISTIC CLASSES AND HOMOGENEOUS SPACES, I.*
Friedrich Hirzebruch;Armand Borel.
American Journal of Mathematics (1958)
Arithmetic subgroups of algebraic groups
Annals of Mathematics (1962)
Corners and arithmetic groups
A. Borel;J-P. Serre.
Commentarii Mathematici Helvetici (1973)
Seminar on transformation groups
Armand Borel;Glen E. Bredon.
Stable real cohomology of arithmetic groups
Annales Scientifiques De L Ecole Normale Superieure (1974)
Compactification of Arithmetic Quotients of Bounded Symmetric Domains
W. L. Baily;A. Borel.
Annals of Mathematics (1966)
Seminar on Algebraic Groups and Related Finite Groups
A. Borel;R. Carter;C. W. Curtis;N. Iwahori.
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