|
Vogtmann
Karen Vogtmann (born July 13, 1949 in Pittsburg, California''Biographies of Candidates 2002.'' . September 2002, Volume 49, Issue 8, pp. 970–981) is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with , an object now known as the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Out(Fn)
In mathematics, Out(''Fn'') is the outer automorphism group of a free group on ''n'' generators. These groups play an important role in geometric group theory. Outer space Out(''Fn'') acts geometrically on a cell complex known as Culler–Vogtmann Outer space, which can be thought of as the Teichmüller space for a bouquet of circles. Definition A point of the outer space is essentially an \R-graph ''X'' homotopy equivalent to a bouquet of ''n'' circles together with a certain choice of a free homotopy class of a homotopy equivalence from ''X'' to the bouquet of ''n'' circles. An \R-graph is just a weighted graph with weights in \R. The sum of all weights should be 1 and all weights should be positive. To avoid ambiguity (and to get a finite dimensional space) it is furthermore required that the valency of each vertex should be at least 3. A more descriptive view avoiding the homotopy equivalence ''f'' is the following. We may fix an identification of the fundamental ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marc Culler
Marc Edward Culler (born November 22, 1953) is an American mathematician who works in geometric group theory and low-dimensional topology. A native Californian, Culler did his undergraduate work at the University of California at Santa Barbara and his graduate work at Berkeley where he graduated in 1978. He is now at the University of Illinois at Chicago. Culler is the son of Glen Jacob Culler who was an important early innovator in the development of the Internet. Work Culler specializes in group theory, low dimensional topology, 3-manifolds, and hyperbolic geometry. Culler frequently collaborates with Peter Shalen and they have co-authored many papers. Culler and Shalen did joint work that related properties of representation varieties of hyperbolic 3-manifold groups to decompositions of 3-manifolds. In particular, Culler and Shalen used the Bass–Serre theory, applied to the function field of the SL(2,C)- Character variety of a 3-manifold, to obtain information about inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Group Theory
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces). Another important idea in geometric group theory is to consider finitely generated groups themselves as geometric objects. This is usually done by studying the Cayley graphs of groups, which, in addition to the graph structure, are endowed with the structure of a metric space, given by the so-called word metric. Geometric group theory, as a distinct area, is relatively new, and became a clearly identifiable branch of mathematics in the late 1980s and early 1990s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, algebraic topology, computational group theory and dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John David Smillie
John David Smillie (born February 18, 1953 in Ithaca, New York) is an American mathematician, specializing in dynamical systems. Biography His father, David Smillie, was a professor of psychology. John Smillie graduated in 1974 with a B.A. in mathematics from New College of Florida. At the university he graduated with an M.S. in 1975 and a Ph.D. in 1977. His Ph.D. thesis ''Affinely flat manifolds'' was supervised by Richard Lashof. From 1977 to 1980 Smillie was an instructor at Princeton University. For the academic year 1980–1981 he was at the Institute for Advanced Study. He was a postdoc for the academic year 1981–1982 at the University of California, Berkeley and for the academic year 1982–1983 at City University of New York (CUNY). At CUNY Smillie was an assistant professor from 1983–1986 and an associate professor from 1986–1989. At Cornell University he was a visiting associate professor from 1986 to 1987, an associate professor from 1987 to December 1990, and a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Bridson
Martin Robert Bridson is a Manx mathematician. He is the Whitehead Professor of Pure Mathematics at the University of Oxford, and President of the Clay Mathematics Institute. He was previously Head of Oxford's Mathematical Institute. He is a Fellow of Magdalen College, Oxford and an Honorary Fellow of Hertford College, Oxford. Specializing in geometry, topology and group theory, Bridson is best known for his work in geometric group theory. Education and early life Bridson is a native of the Isle of Man. He was educated at St Ninian's High School, Douglas, then Hertford College, Oxford, and Cornell University, receiving a Master of Arts degree from Oxford in 1986, and a Master of Science degree in 1988 followed by a PhD in 1991 from Cornell. His PhD thesis was supervised by Karen Vogtmann, and was entitled ''Geodesics and Curvature in Metric Simplicial Complexes''. Career and research He was an assistant professor at Princeton University until 1996, was twice a visiting pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noether Lecture
The Noether Lecture is a distinguished lecture series that honors women "who have made fundamental and sustained contributions to the mathematical sciences". The Association for Women in Mathematics (AWM) established the annual lectures in 1980 as the Emmy Noether Lectures, in honor of one of the leading mathematicians of her time. In 2013 it was renamed the AWM-AMS Noether Lecture and since 2015 is sponsored jointly with the American Mathematical Society (AMS). The recipient delivers the lecture at the yearly American Joint Mathematics Meetings held in January. The ICM Emmy Noether Lecture is an additional lecture series, sponsored by the International Mathematical Union. Beginning in 1994 this lecture was delivered at the International Congress of Mathematicians, held every four years. In 2010 the lecture series was made permanent. The 2021 Noether Lecture was supposed to have been given by Andrea Bertozzi of UCLA, but it was cancelled due to Bertozzi's connections to policing. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pittsburg, California
Pittsburg is a city in Contra Costa County, California, United States. It is an industrial suburb located on the southern shore of the Suisun Bay in the East Bay region of the San Francisco Bay Area, and is part of the Sacramento–San Joaquin River Delta area. The population was 76,416 at the 2020 United States Census. History Originally settled in 1839 as “Rancho Los Medanos”, the area of almost 10,000 acres was issued to Californios Jose Antonio Mesa and his brother Jose Miguel under a Mexican Land Grant by then Governor Juan Bautista Alvarado, one of the final land grants issued prior to the formation of California as a state. In 1849, during the California Gold Rush, Colonel Jonathan D. Stevenson (from New York) bought the Rancho Los Medanos land grant for speculation, and laid out a town he called New York of the Pacific. General William Tecumsah Sherman laid out the first network of streets on the west side of town. The area was the midway stopping point for schoon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debra Boutin
Debra Lynn Boutin is an American mathematician, the Samuel F. Pratt Professor of Mathematics at Hamilton College, where she chairs the mathematics department. Her research involves the symmetries of graphs and distinguishing colorings of graphs. Education and career Boutin is a graduate of Chicopee Comprehensive High School in Massachusetts. After high school, Boutin took a ten-year hiatus from higher education, including serving for four years in the United States Navy, working as a secretary, and raising a child. She restarted her education, supported by the G.I. Bill, by studying data processing at Springfield Technical Community College in Massachusetts. Next, Boutin went to Smith College as an Ada Comstock Scholar. She graduated Phi Beta Kappa and summa cum laude in 1991 with a bachelor's degree in mathematics. She completed her Ph.D. in mathematics in 1998 at Cornell University. Her doctoral dissertation, ''Centralizers of Finite Subgroups of Automorphisms and Outer Automor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenilworth
Kenilworth ( ) is a market town and civil parish in the Warwick District in Warwickshire, England, south-west of Coventry, north of Warwick and north-west of London. It lies on Finham Brook, a tributary of the River Sowe, which joins the River Avon north-east of the town. At the 2021 Census, the population was 22,538. The town is home to the ruins of Kenilworth Castle and Kenilworth Abbey. History Medieval and Tudor A settlement existed at Kenilworth by the time of the 1086 Domesday Book, which records it as ''Chinewrde''. Geoffrey de Clinton (died 1134) initiated the building of an Augustinian priory in 1122, which coincided with his initiation of Kenilworth Castle. The priory was raised to the rank of an abbey in 1450 and suppressed with the Dissolution of the Monasteries in the 1530s. Thereafter, the abbey grounds next to the castle were made common land in exchange for what Robert Dudley, 1st Earl of Leicester used to enlarge the castle. Only a few walls an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a set and an operation that combines any two elements of the set to produce a third element of the set, in such a way that the operation is associative, an identity element exists and every element has an inverse. These three axioms hold for number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the '' Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
