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Piecewise Algebraic Space
In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation was for the proof of Deligne's conjecture on Hochschild cohomology In deformation theory, a branch of mathematics, Deligne's conjecture is about the operadic structure on Hochschild cochain complex. Various proofs have been suggested by Dmitry Tamarkin, Alexander A. Voronov, James E. McClure and Jeffrey H. Sm .... Robert Hardt, Pascal Lambrechts, Victor Turchin, and Ismar Volić later developed the theory. References * * Maxim Kontsevich and Yan Soibelman. “Deformations of algebras over operads and the Deligne conjecture”. In: Conférence Moshé Flato 1999, Vol. I (Dijon). Vol. 21. Math. Phys. Stud. Dordrecht: Kluwer Acad. Publ., 2000, pp. 255–307. arXiv: math/0001151. {{geometry-stub Algebraic geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semialgebraic Set
In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are mainly studied in real algebraic geometry which is the appropriate framework for algebraic geometry over the real numbers. Definition Let \mathbb be a real closed field (For example \mathbb could be the field of real numbers \mathbb). A subset S of \mathbb^n is a ''semialgebraic set'' if it is a finite union of sets defined by polynomial equalities of the form \ and of sets defined by polynomial inequalities of the form \. Properties Similarly to algebraic subvarieties, finite unions and intersections of semialgebraic sets are still semialgebraic sets. Furthermore, unlike subvarieties, the complement of a semialgebraic set is again semialgebraic. Finally, and most importantly, the Tarski–Seide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxim Kontsevich
Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Breakthrough Prize in Fundamental Physics in 2012, and the Breakthrough Prize in Mathematics in 2015. Academic career and research He was born into the family of Lev Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Information Transmission Problems in Moscow. While at the institute he published papers that caught the interest of the Max Planck Institute in Bonn and was invited for three months. Just before the end of his time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yan Soibelman
Iakov (Yan) Soibelman (Russian: Яков Семенович Сойбельман) born 15 April 1956 (Kiev, USSR) is a Russian American mathematician, professor at Kansas State University (Manhattan, USA), member of thKyiv Mathematical Society(Ukraine), founder of Manhattan Mathematical Olympiad. Scientific work Yan Soibelman is a specialist in theory of quantum groups, representation theory and symplectic geometry. He introduced the notion of quantum Weyl group, studied representation theory of the algebras of functions on compact quantum groups, and meromorphic braided monoidal categories. His long term collaboration with Maxim Kontsevich is devoted to various aspects of homological mirror symmetry, a proof of Deligne conjecture about operations on the cohomological Hochschild complex, a direct construction of Calabi-Yau varieties based on SYZ conjecture The SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deligne's Conjecture On Hochschild Cohomology
In deformation theory, a branch of mathematics, Deligne's conjecture is about the operadic structure on Hochschild cochain complex. Various proofs have been suggested by Dmitry Tamarkin, Alexander A. Voronov, James E. McClure and Jeffrey H. Smith, Maxim Kontsevich and Yan Soibelman, and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex. It is of importance in relation with string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera .... See also * Piecewise algebraic space References {{reflist Further reading * https://ncatlab.org/nlab/show/Deligne+conjecture * https://mathoverflow.net/questions/374/delignes-conjecture-the-little-discs-operad-one Algebraic topology String theory Conjectures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ismar Volić
Ismar Volić is a Bosnian-American mathematician. He is a professor of mathematics at Wellesley College and a co-founder of the Institute for Mathematics and Democracy. Education and career Volić completed his undergraduate degree at Boston University in 1998 and his Ph.D. in mathematics at Brown University in 2003 under the direction of Thomas Goodwillie. He was a Whyburn Research Instructor at the University of Virginia from 2003 to 2006. He has been teaching at Wellesley College since 2006. He was the department chair from 2022 to 2025. He was a visiting professor at MIT, Louvain-la-Neuve University, and the University of Virginia. In 2019, he co-founded the Institute for Mathematics and Democracy to "promote a deeper understanding of mathematics as a pivotal force in creating a democracy where people make informed political decisions and enact change based on objective and rigorous quantitative criteria". Volić is an active member of the Bosnian-Herzegovinian American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |