Combinatorialists at UW
The department currently has a very active group in combinatorics with
a long history of excellence in this field beginning with E.T.Bell.
During the latter half of the 20th century, Branko Grünbaum and
Victor Klee, played an important role in establishing the field of
combinatorics through their seminal work on geometric combinatorics
and the connections to computer science, operations research and pure
mathematics. With the impending retirements of Grünbaum and
Klee, in 1997 and 2000, the department placed a high priority in the
late 90's on maintaining this strong reputation through selective
hiring in algebraic, geometric, and probabalistic combinatorics. The
department has now assembled an active group of researchers in
this field, consisting of professors Rekha Thomas (hired in 2000),
Sara Billey (hired in 2002) and Isabella Novik (hired in 2004).
Assistant Professor Ioana Dumitriu was appointed in 2006. Chris
Hoffman started out in ergotic theory and has moved closer to
probabalisitc combinatorics through his work with Yuval Peres at
Microsoft. The combinatorics group is further bolstered by faculty in
related areas including representation theory, algebraic geometry,
optimization, probability, algebra, and our affiliate faculty in the
Microsoft theory group with interests in combinatorics. We have a
weekly seminar in combinatorics in addition to undergraduate and
topics courses in this area every year. We regularly run a year long
graduate course entitled "Foundations of Combinatorics" for students
interested in the area.
Billey's research is at the intersection of algebraic
combinatorics, Lie theory, computational algebraic geometry, probability
and experimental mathematics. More specifically, that includes affine
Grassmannians, Schubert varieties, Schubert polynomials, flag
manifolds, symmetric functions, root systems, Coxeter groups, diagonal
harmonics, computer aided combinatorics, stochastic processes, complexity
theory, fingerprint databases, and learning algorithms.
The research interests of Isabella Novik lie in combinatorics
of simplicial complexes, and in connections between combinatorics,
commutative algebra, and algebraic topology. Her work includes
problems related to characterizing face numbers for various classes
of simplicial complexes.
Rekha Thomas works on problems that lie at the intersection of
optimization, computational algebra and geometry.
Chris Hoffman works at the intesection of combinatorics with
Ioana Dumitriu's research interests include random matrices,
computing, and algorithmic game theory.
Thomas Rothvoss's research interests are discrete optimization, linear/integer programming and theoretical computer science.