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Alexander Grothendieck was a French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.
John Willard Milnor is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize and all three Steele prizes.
In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of abstract algebra. The modern theory of pseudogroups was developed by Élie Cartan in the early 1900s.
Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad , one defines an algebra over to be a set together with concrete operations on this set which behave just like the abstract operations of . For instance, there is a Lie operad such that the algebras over are precisely the Lie algebras; in a sense abstractly encodes the operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group representations.
In category theory, a branch of mathematics, a PROP is a symmetric strict monoidal category whose objects are the natural numbers n identified with the finite sets and whose tensor product is given on objects by the addition on numbers. Because of “symmetric”, for each n, the symmetric group on n letters is given as a subgroup of the automorphism group of n. The name PROP is an abbreviation of "PROduct and Permutation category".
Shlomo Zvi Sternberg, is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory.
Fondements de la Géometrie Algébrique (FGA) is a book that collected together seminar notes of Alexander Grothendieck. It is an important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry in its modern technical developments. The title is a translation of the title of André Weil's book Foundations of Algebraic Geometry. It contained material on descent theory, and existence theorems including that for the Hilbert scheme. The Technique de descente et théorèmes d'existence en géometrie algébrique is one series of seminars within FGA.
Victor William Guillemin is an American mathematician. He works at the Massachusetts Institute of Technology in the field of symplectic geometry, and he has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics.
In the theory of operads in algebra and algebraic topology, an A∞-operad is a parameter space for a multiplication map that is homotopy coherently associative.
In the theory of operads in algebra and algebraic topology, an E∞-operad is a parameter space for a multiplication map that is associative and commutative "up to all higher homotopies".
This is a timeline of category theory and related mathematics. Its scope is taken as:
In mathematics, especially (higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra.
"Esquisse d'un Programme" is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. Grothendieck's vision provides inspiration today for several developments in mathematics such as the extension and generalization of Galois theory, which is currently being extended based on his original proposal.
Mikhail "Mischa" Gershevich Katz is an Israeli mathematician, a professor of mathematics at Bar-Ilan University. His main interests are differential geometry, geometric topology and mathematics education; he is the author of the book Systolic Geometry and Topology, which is mainly about systolic geometry. The Katz–Sabourau inequality is named after him and Stéphane Sabourau.
In geometry, the cyclohedron is a -dimensional polytope where can be any non-negative integer. It was first introduced as a combinatorial object by Raoul Bott and Clifford Taubes and, for this reason, it is also sometimes called the Bott–Taubes polytope. It was later constructed as a polytope by Martin Markl and by Rodica Simion. Rodica Simion describes this polytope as an associahedron of type B.
James Dillon Stasheff is an American mathematician, a professor emeritus of mathematics at the University of North Carolina at Chapel Hill. He works in algebraic topology and algebra as well as their applications to physics.
Ralph Martin Kaufmann is a German mathematician working in the United States.
Alexander A. Voronov is a Russian-American mathematician specializing in mathematical physics, algebraic topology, and algebraic geometry. He is currently a Professor of Mathematics at the University of Minnesota and a Visiting Senior Scientist at the Kavli Institute for the Physics and Mathematics of the Universe.
References
- ↑ "Prof. Steven Shnider - staff page" (in Hebrew). Bar Ilan University. Archived from the original on 2011-02-21. Retrieved 2010-01-21.
- ↑ Steven David Shnider, Mathematics Genealogy Project. Accessed January 24, 2010
- ↑ Meeting in honor of Steve Shnider's Retirement. Bar Ilan University. Accessed June 28, 2019
- ↑ Alexander A. Voronov. "Review of Operads in algebra, topology and physics". Mathematical Reviews. MR 1898414.
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