Profiles

 

Short Profile


Dr. Higson is a specialist in noncommutative geometry, which is a relatively new subject that examines mathematical and physical phenomena using matrix techniques.  There are close connections between noncommutative geometry and quantum theory, where matrix algebra methods are pervasive.  In addition, noncommutative geometry brings the same tools to classical mathematical and physical problems.  Exemplifying this is Higson's work on the Novikov conjecture, in which infinite-dimensional matrix analysis is brought to bear on a major problem in classical topology.  In recognition of his research accomplishments, Dr. Higson was elected a Fellow of the Royal Society of Canada in 2000.  Higson has also distinguished himself as an outstanding teacher.  He has an engaging sense of humor and he is known for his ability to spontaneously develop analogies and examples that help his students to learn.  In 2001 he received Penn State's Atherton Award for excellence in teaching.  Dr. Higson served as head of the Department of Mathematics at Penn State from 2003 to 2006.



Medium Profile


Nigel Higson is Evan Pugh Professor of Mathematics at the Pennsylvania State University.


Professor Higson's research specialty is operator algebra theory, a subject with roots in the mathematical foundations of quantum theory and in Fourier analysis. These two antecedents have come to be synthesized in a remarkable way, with quite powerful consequences in topology and geometry. Professor Higson's recent work has focussed on the Baum-Connes conjecture, a broad program that connects operator algebra theory to problems in differential topology, Riemannian geometry, and various areas of representation theory. Along with Paul Baum and Alain Connes, Higson is responsible for the current form of the conjecture.


Professor Higson's research and teaching accomplishments have been regularly recognized, both nationally and internationally. He was awarded a Sloan Fellowship and won Canada's Aisenstadt Medal and its Coxeter-James and Halperin Prizes, all of which recognize young mathematicians who have made outstanding contributions to mathematical research. He has delivered plenary addresses to the American, Australian and Canadian Mathematical Societies, and in 1998 he delivered an invited lecture to the International Congress of Mathematicians in Berlin. He was a Clay Mathematics Institute Prize Fellow in 1999 and in 2000 was elected a fellow of the Royal Society of Canada.  At Penn State he has received the C.I. Noll and Atherton Awards for excellence in teaching.


Higson earned three degrees at Dalhousie University in Halifax, Nova Scotia - a bachelor of arts in 1982, master of science in 1983 and doctoral degree in 1986. He was a postdoctoral fellow at Dalhousie in 1986.  From 1986 to 1990, Higson was an assistant professor at the University of Pennsylvania. He joined the Penn State faculty as an assistant professor in 1989.  He was promoted to associate professor in 1990 and professor in 1994.  He was named Distinguished Professor of Mathematics in 2000 and in 2006 he was named Evan Pugh Professor of Mathematics.  Professor Higson has held visiting appointments at several universities in North America and Europe, including the Stanislaw Ulam professorship at the University of Colorado in 1996.  He served as head of the Penn State Department of Mathematics from 2003 to 2006.



Long Informal Profile


It is an early spring morning, and although the air is cool, drops of sweat trickle down Nigel Higson's face.  His lungs burn as he propels himself up the mountain on his bicycle.  "If you're struggling to get to the top of a mountain, you really can't think about anything else," said Higson, Evan Pugh Professor of Mathematics at Penn State.  "I find cycling to be very calming in this way."


Higson, who regularly bicycles long distances in his free time, is particularly deserving of the mental breaks that the sport affords him.  After all, he is a mathematician who spends much of his time thinking about abstract ideas like infinite-dimensional matrices -- groups of numbers ordered in infinitely many rows and columns.  "The numbers in a matrix are shorthand for a collection of equations," said Higson.  "Although infinite-dimensional matrices are abstract concepts, I spent my entire graduate-school career learning how to treat things that have no real existence as concrete objects.  So, I have no difficulty thinking of a system of infinite-by-infinite matrices as a completely concrete object like a can of beans."


The ability to comprehend complicated mathematical ideas is a talent that Higson began to develop at an early age.  "I always knew I would be a mathematician," he said.  "I remember being exceedingly good at fractions and solving other kids' homework for them just because I enjoyed it."


Higson's research involves solving the equations associated with infinite-dimensional matrices.  "Imagine that you have a matrix equation that contains an unknown variable, V.  I would ask, for example, if it is the case that the equation can be solved for every possible V.  It is not always possible to solve every single equation.  If the equation can be solved, I might then ask how many different ways it can be solved.  Or maybe I might ask if there are Vs for which V itself is a solution to the matrix equation."


In addition to infinite-dimensional matrices, Higson also studies operator-algebra theory, a subject that has roots in the mathematical foundations of quantum theory and in Fourier analysis, and that also has powerful consequences in the fields of topology and geometry.  He and his colleagues are responsible for the current form of the Baum-Connes conjecture, a broad program that connects operator-algebra theory to problems in other areas of mathematics.  Higson's goal is to use the equations to make connections between various parts of modern mathematics.


Higson earned his bachelor's, master's, and doctoral degrees at Dalhousie University in Halifax, Nova Scotia.  From 1986 to 1990, he was an assistant professor at the University of Pennsylvania.  He joined the Penn State faculty as an assistant professor in 1989 and was promoted to associate professor in 1990 and to professor in 1994.  He was named distinguished professor of mathematics in 2000 and an Evan Pugh professor in 2006.


Higson has received much recognition for his research, including a Sloan Foundation Fellowship in 1992, the André Aisenstadt Prize of the Center for Mathematical Research in Montreal in 1995, the Israel Halperin Prize of the Canadian Operator Symposium in 1995, and the Coxeter James Prize of the Canadian Mathematical Society in 1996.  In addition, he was elected a Fellow of the Academy of Sciences of the Royal Society of Canada in 2000.


Higson also is an accomplished and popular teacher, and he places teaching at the top of his list of most rewarding activities.  "I really have a great time in front of the class," he said.  "I just love to talk about mathematics.  I'm not very good at cocktail parties, but I can prattle on about mathematics forever."


Mathematics, however, is hardly the stuff of idle chatter.  To Higson, conducting mathematical research is akin to writing poetry and composing music.  "What distinguishes us from other species is our brains," he said.  "It is the collective creative accomplishments of our species that we are most proud of.  The beautiful music that we have composed, the poetry that we have written, the art that we have created, and the knowledge that we have acquired, that's what it means to be a person.  That's the mark that we have made on the universe."


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