Andrew John Casson FRS (born 1943) is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, studying

geometric topology In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topo ...

. Casson is the Philip Schuyler Beebe Professor of Mathematics at

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

Education and career

Casson was educated at

Latymer Upper School Latymer Upper School is a public school in Hammersmith, London, England, on King Street. It derives from a charity school, and is part of the same 1624 Latymer Foundation, from a bequest by the English legal official Edward Latymer. There ...

and

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, where he graduated with a BA in the Mathematical Tripos in 1965.'University News: Cambridge Tripos Results', ''Times'', 21 June 1965. His doctoral advisor at the

University of Liverpool The University of Liverpool (abbreviated UOL) is a Public university, public research university in Liverpool, England. Founded in 1881 as University College Liverpool, Victoria University (United Kingdom), Victoria University, it received Ro ...

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. Casson was Professor of Mathematics at the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...

between 1981 and 1986, at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, from 1986 to 2000, and has been at Yale since 2000.

Work

Casson has worked in both high-dimensional manifold topology and 3- and 4-dimensional

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, using both geometric and algebraic techniques. Among other discoveries, he contributed to the disproof of the manifold

Hauptvermutung The ''Hauptvermutung'' of geometric topology is a now refuted conjecture asking whether any two Triangulation (topology), triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulati ...

, introduced the Casson invariant, a modern invariant for 3-

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s, and Casson handles, used in

Michael Freedman Michael Hartley Freedman (born April 21, 1951) is an American 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 4-dimensional gen ...

's proof of the 4-dimensional

Poincaré conjecture In the mathematical field of geometric topology, the Poincaré conjecture (, , ) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured b ...

Awards

In 1991, he was awarded the Oswald Veblen Prize in Geometry by the

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, ...

. In 1998, he was elected to Fellowship of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

References

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.

* 1943 births Living people Fellows of the Royal Society Alumni of Trinity College, Cambridge University of Texas at Austin faculty University of California, Berkeley College of Letters and Science faculty Yale University faculty Topologists Alumni of the University of Liverpool {{mathematician-stub