Andrew Casson
Encyclopedia
Andrew John Casson FRS (born 1943) is a mathematician
, an expert on geometric topology
.
Casson is the Philip Schuyler Beebe Professor of Mathematics at Yale University
in the United States
where he served as department chair between 2004 and 2007. His Ph.D. advisor at the University of Liverpool
was C. T. C. Wall
, but he never completed his doctorate; instead what would have been his Ph.D. thesis became his fellowship dissertation as a research fellow at Trinity College, Cambridge. He was Professor of Mathematics at the University of Texas at Austin
between 1981 and 1986, at the University of California, Berkeley
from 1986 to 1999, and has been at Yale since 2000.
In 1991, he was awarded the Oswald Veblen Prize in Geometry
by the American Mathematical Society
. In 1998 he was elected to Fellowship of the Royal Society
.
Casson has worked in both high-dimensional manifold topology and 3 and 4 dimensional topology,
using both geometric and algebraic techniques. Among other discoveries, he contributed
significantly to the disproof of the manifold Hauptvermutung
, introduced the Casson invariant
, an important modern invariant for 3-manifold
s, and Casson handle
s, used in Freedman's
proof of the 4-dimensional Poincaré conjecture
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, an expert on geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
.
Casson is the Philip Schuyler Beebe Professor of Mathematics at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
where he served as department chair between 2004 and 2007. His Ph.D. advisor at the University of Liverpool
University of Liverpool
The University of Liverpool is a teaching and research university in the city of Liverpool, England. It is a member of the Russell Group of large research-intensive universities and the N8 Group for research collaboration. Founded in 1881 , it is also one of the six original "red brick" civic...
was C. T. C. Wall
C. T. C. Wall
Charles Terence Clegg Wall is a leading British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed Professor in 1965...
, but he never completed his doctorate; instead what would have been his Ph.D. thesis became his fellowship dissertation as a research fellow at Trinity College, Cambridge. He was Professor of Mathematics at the University of Texas at Austin
University of Texas at Austin
The University of Texas at Austin is a state research university located in Austin, Texas, USA, and is the flagship institution of the The University of Texas System. Founded in 1883, its campus is located approximately from the Texas State Capitol in Austin...
between 1981 and 1986, at 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...
from 1986 to 1999, and has been at Yale since 2000.
In 1991, he was awarded the Oswald Veblen Prize in Geometry
Oswald Veblen Prize in Geometry
The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen...
by the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
. In 1998 he was elected to Fellowship of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
.
Casson has worked in both high-dimensional manifold topology and 3 and 4 dimensional topology,
using both geometric and algebraic techniques. Among other discoveries, he contributed
significantly to the disproof of the manifold Hauptvermutung
Hauptvermutung
The Hauptvermutung of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze.This conjecture is now known to be false...
, introduced the Casson invariant
Casson invariant
In 3-dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer-valued invariant of oriented integral homology 3-spheres, introduced by Andrew Casson....
, an important modern invariant for 3-manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s, and Casson handle
Casson handle
In 4-dimensional topology, a branch of mathematics, a Casson handle is a 4-dimensional topological 2-handle constructed by an infinite procedure. They are named for Andrew Casson, who introduced them in about 1973. They were originally called "flexible handles" by Casson himself, and introduced...
s, used in Freedman's
Michael Freedman
Michael Hartley Freedman is a mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists.Freedman was born...
proof of the 4-dimensional Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
.
External links
- Official Home Page
- The Hauptvermutung book (including Casson's 1967 Trinity College fellowship dissertation)
- Proceedings of the Casson Fest (Arkansas and Texas 2003) A conference to celebrate Casson's 60th birthday, with biographical information.
- Photos from conference, including the `honorary degree' presented to Casson by the participants