William Menasco
Encyclopedia
William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory
.
from the University of California, Los Angeles
in 1975, and his Ph.D.
from the University of California, Berkeley
in 1981, where his advisor was Robion Kirby
. He served as assistant professor at Rutgers University
from 1981 to 1984. He then taught as a visiting professor at the University at Buffalo where he became an assistant professor in 1985, an associate professor in 1991. In 1994 he became a professor at the University at Buffalo where he currently serves.
with an alternating diagram, such as an alternating link, will be non-split
if and only if the diagram is connected.
Menasco, along with Morwen Thistlethwaite
proved the Tait flyping conjecture
, which states that given any two reduced alternating diagrams D1,D2 of an oriented, prime alternating link, D1 may be transformed to D2 by means of a sequence of certain simple moves called flype
s.
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
.
Biography
Menasco received is B.A.Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
from the University of California, Los Angeles
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
in 1975, and his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
in 1981, where his advisor was Robion Kirby
Robion Kirby
Robion Cromwell Kirby is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology...
. He served as assistant professor at Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
from 1981 to 1984. He then taught as a visiting professor at the University at Buffalo where he became an assistant professor in 1985, an associate professor in 1991. In 1994 he became a professor at the University at Buffalo where he currently serves.
Work
Menasco proved that a linkLink (knot theory)
In mathematics, a link is a collection of knots which do not intersect, but which may be linked together. A knot can be described as a link with one component. Links and knots are studied in a branch of mathematics called knot theory...
with an alternating diagram, such as an alternating link, will be non-split
Split link
In the mathematical field of knot theory, a split link is a link that has a 2-sphere in its complement separating one or more link components from the others. A split link is said to be splittable, and a link that is not split is called a non-split link or not splittable...
if and only if the diagram is connected.
Menasco, along with Morwen Thistlethwaite
Morwen Thistlethwaite
Morwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory, and Rubik's cube group theory.-Biography:...
proved the Tait flyping conjecture
Tait conjectures
The Tait conjectures are conjectures made by Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe...
, which states that given any two reduced alternating diagrams D1,D2 of an oriented, prime alternating link, D1 may be transformed to D2 by means of a sequence of certain simple moves called flype
Flype
In the mathematical theory of knots, a flype is a kind of manipulation of knot and link diagramsused in the Tait flyping conjecture.It consists of twisting a part of a knot, a tangle: T by 180 degrees. Flype comes from an old Scottish word meaning to fold or to turn back. Two reduced alternating...
s.
External links
- http://www.math.buffalo.edu/~menasco/ — William Menasco's home page.