John Willard Milnor is an American mathematician known for his work in differential topology, K-theory and dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn.
In mathematics, the symbolic method in invariant theory is an algorithm developed by Arthur Cayley, Siegfried Heinrich Aronhold, Alfred Clebsch, and Paul Gordan in the 19th century for computing invariants of algebraic forms. It is based on treating the form as if it were a power of a degree one form, which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it.
Jean Alexandre Eugène Dieudonné was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology. His work on the classical groups, and on formal groups, introducing what now are called Dieudonné modules, had a major effect on those fields.
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
Bertram Kostant was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and was Director of the Mathematical Sciences Research Institute (MSRI) from 1997 to 2007. He was reappointed to this office in 2013, and his term has been extended until July 31, 2022.
Conjeevaram Srirangachari SeshadriFRS was an Indian mathematician. He was the founder and director-emeritus of the Chennai Mathematical Institute, and is known for his work in algebraic geometry. The Seshadri constant is named after him. He was also known for his collaboration with mathematician M. S. Narasimhan, for their proof of the Narasimhan–Seshadri theorem which proved the necessary conditions for stable vector bundles on a Riemann surface.
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.
William Edgar Fulton is an American mathematician, specializing in algebraic geometry.
Sigurdur Helgason is an Icelandic mathematician whose research has been devoted to the geometry and analysis on symmetric spaces. In particular he has used new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces as well as some new results on the representations of their isometry groups. He also introduced a Fourier transform on these spaces and proved the principal theorems for this transform, the inversion formula, the Plancherel theorem and the analog of the Paley–Wiener theorem.
Kai Behrend is a German mathematician. He is a professor at the University of British Columbia in Vancouver, British Columbia, Canada.
In mathematics, the Chevalley–Iwahori–Nagata theorem states that if a linear algebraic group G is acting linearly on a finite-dimensional vector space V, then the map from V/G to the spectrum of the ring of invariant polynomials is an isomorphism if this ring is finitely generated and all orbits of G on V are closed. It is named after Claude Chevalley, Nagayoshi Iwahori, and Masayoshi Nagata.
In mathematics, the Young–Deruyts development is a method of writing invariants of an action of a group on an n-dimensional vector space V in terms of invariants depending on at most n–1 vectors.
In mathematics, Gram's theorem states that an algebraic set in a finite-dimensional vector space invariant under some linear group can be defined by absolute invariants.. It is named after J. P. Gram, who published it in 1874.
In mathematics, the Hilbert–Mumford criterion, introduced by David Hilbert and David Mumford, characterizes the semistable and stable points of a group action on a vector space in terms of eigenvalues of 1-parameter subgroups.
In mathematics, the bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d-by-d minors of a generic d-by-n matrix (xij).
In mathematics, a nullform of a vector space acted on linearly by a group is a vector on which all invariants of the group vanish. Nullforms were introduced by Hilbert (1893)..
Claudio Procesi is an Italian mathematician, known for works in algebra and representation theory.
Vinayak Vatsal is a Canadian mathematician working in number theory and arithmetic geometry.
