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David J. Benson
Distinguished Research Professor of Mathematics
Lamar Dodd
Award 2004
Distinguished
Research Professor 2000
Creative Research
Medal 1998
David J. Benson, Distinguished Research Professor of Mathematics,
is internationally recognized for important contributions to basic
mathematical research, particularly in the areas of algebra and
topology.
“He is quite unique in the way his work depends and uses the two
different areas – [algebra and topology] – so very successfully.
Such breadth and great depth at the same time is rare,” wrote Jonathan
Alperin, mathematics professor at the University of Chicago.
In a broad sense, Dr. Benson’s research centers around the study
of symmetry. He takes an abstract pattern of potential symmetries,
called a group, and attempts to understand all the algebraic and
topological objects that admit this abstract pattern as a collection
of symmetries. If the object is linear in nature, this is called
a representation. Cohomology is the glue between representations,
and is also the link between the algebra and the topology.
His interests cover broad areas including finite group theory,
representation theory, cohomology of groups, algebraic topology,
commutative algebra and invariant theory. His work is at the forefront
of a branch of algebra called cohomology of finite groups, which
has applications in chemistry and physics. Dr. Benson has written
four books related to subjects dealing with representation theory
and cohomology with connections to algebraic topology. His two-volume
series on representations and cohomology has become a standard
reference tool. In addition, he is writing a book on music and
mathematics based on the course he developed on that topic at UGA.
“In papers written jointly with [UGA mathematician] Jon Carlson,
they laid the groundwork for a precise and practical geometric
understanding of group cohomology via the use of cohomological
varieties,” wrote Alejandro Adem, mathematics professor at the
University of Wisconsin. “By combining techniques from algebraic
geometry with representation theory, they developed easily applicable
and powerful methods which have had a broad impact not only in
group cohomology but which also have been applied successfully
to difficult problems in topological transformation groups. Almost
all recent progress in the field depends heavily on their work
and it would be hard to overestimate the value of the Benson-Carlson
techniques.”
Dr. Benson was awarded the London Mathematical Society’s 1993
Junior Whitehead Prize, a 1998 UGA Creative Research Medal, and
a UGA Distinguished Research Professorship in 2000. Dr.
Benson has received continuous funding from the National Science
Foundation since 1994.
Source: 25th Annual Research
Awards Program (2004)
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