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## Faculty Research Interests

Shabnam Akhtari:
number theory, Diophantine equations.

Arkady Berenstein:
quantum groups, representation theory, algebraic combinatorics.

Boris Botvinnik:
differential topology, positive scalar curvature, Morse theory.

Marcin Bownik:
harmonic analysis, wavelets, approximation theory.

Jon Brundan:
algebraic groups, combinatorial representation theory,
Lie superalgebras.

Dan Dugger:
motivic homotopy theory, K-theory, homological algebra.

Peter Gilkey:
higher-signature differential geometry, heat trace analysis.

Weiyong He:
differential geometry and partial differential equations.

Jim Isenberg:
mathematical general relativity, Ricci flow, nonlinear PDEs.

Alexander Kleshchev:
representation theory, Lie theory, group theory.

David Levin:
Markov chains and random walks, multiparameter processes,
potential theory.

Shlomo Libeskind:
mathematics education.

Huaxin Lin:
Functional analysis, C*-algebras, dynamical systems.

Peng Lu:
geometric analysis, Ricci flow, complex geoemtry.

Victor Ostrik:
geometric Lie theory, tensor categories, Hopf algebras.

N. Christopher Phillips:
C*-algebras, functional analysis, noncommutative geometry.

Alexander Polischuk:
algebraic geometry, noncommutative tori,
mathematics related to string theory.

Nicholas Proudfoot:
symplectic algebraic geometry, matroid theory, quivers.

Hal Sadofsky:
stable homotopy theory, homological algebra, complex cobordism.

Brad Shelton:
non-commutative algebraic geometry, ring theory, homological algebra.

Chris Sinclair:
random matrix theory, heights of polynomials.

Dev Sinha:
rational homotopy theory, knot theory, operads.

Bartlomiej Siudeja:
probability, differential equations.

Arkady Vaintrob:
algebraic geometry, knot theory, mathematical physics, Lie theory.

Marie Vitulli:
commutative algebra, closure operations, valuation theory,
algebraic geometry.

Vadim Vologodsky:
algebraic geometry, homological algebra.

Hao Wang:
superprocesses, mathematical finance, stochastic PDEs.

Micah Warren:
geometric analysis, nonlinear elliptic PDEs.

Yuan Xu:
numerical analysis, orthogonal polynomials,
approximation theory, harmonic analysis.

Ben Young:
algebraic and enumerative combinatorics,
perfect matchings.

Sergey Yuzvinsky:
algebraic combinatorics, hyperplane arrangements,
algebraic geometry and topology.