|
Zimmer's Conjecture
Zimmer's conjecture is a statement in mathematics "which has to do with the circumstances under which geometric spaces exhibit certain kinds of symmetries." It was named after the mathematician Robert Zimmer. The conjecture states that there can exist symmetries (specifically higher-rank lattices) in a higher dimension that cannot exist in lower dimensions. In 2017, the conjecture was proven by Aaron Brown and Sebastián Hurtado-Salazar of the University of Chicago and David Fisher of Indiana University Indiana University (IU) is a system of public universities in the U.S. state of Indiana. Campuses Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI. * Indiana Univers .... References Symmetry Conjectures that have been proved {{math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Space
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Zimmer
Robert Jeffrey Zimmer (born November 5, 1947) is an American mathematician and academic administrator. From 2006 until 2021, he served as the 13th president of the University of Chicago and as the Chair of the Board for Argonne National Lab, Fermi National Accelerator Laboratory, and the Marine Biological Laboratory. He then served as chancellor of the University of Chicago until July 2022. As a mathematician, Zimmer specializes in geometry, particularly ergodic theory, Lie groups, and differential geometry. Education and work experience Zimmer graduated from New York's Stuyvesant High School in 1964. He matriculated to Brandeis University as an undergraduate, earning his B.A., summa cum laude, in 1968. He conducted his mathematics graduate study at Harvard University, receiving his master's degree in 1971 and his Ph.D. in 1975 under the supervision of George Mackey. Zimmer taught at the United States Naval Academy from 1975 to 1977, and moved to the mathematics department of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Chicago
The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chicago is consistently ranked among the best universities in the world and it is among the most selective in the United States. The university is composed of College of the University of Chicago, an undergraduate college and five graduate research divisions, which contain all of the university's graduate programs and interdisciplinary committees. Chicago has eight professional schools: the University of Chicago Law School, Law School, the Booth School of Business, the Pritzker School of Medicine, the Crown Family School of Social Work, Policy, and Practice, the Harris School of Public Policy, the University of Chicago Divinity School, Divinity School, the Graham School of Continuing Liberal and Professional Studies, and the Pritzker School of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indiana University
Indiana University (IU) is a system of public universities in the U.S. state of Indiana. Campuses Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI. * Indiana University Bloomington (IU Bloomington) is the flagship campus of Indiana University. The Bloomington campus is home to numerous premier Indiana University schools, including the College of Arts and Sciences, the Jacobs School of Music, an extension of the Indiana University School of Medicine, the School of Informatics, Computing, and Engineering, which includes the former School of Library and Information Science (now Department of Library and Information Science), School of Optometry, the O'Neil School of Public and Environmental Affairs, the Maurer School of Law, the School of Education, and the Kelley School of Business. * Indiana University–Purdue University Indianapolis (IUPUI), a partnership between Indiana University and Purdue Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Symmetry")
