Hongyu He 

Harmonic Analysis on Classical Groups, Representation Theory, Geometry on Homogeneous Spaces, Combinatorics, Computational Biology. 
Jimmie Lawson 

Lie Semigroup Theory, Geometry on Symmetric Spaces of Nonpositive Curvature, Geometric Control Theory on Lie Groups and Coset Spaces. 
Gestur Olafsson 

Harmonic analysis on homogeneous spaces, integral transforms such as the Radon transform, wavelets and wavelet sets, representation theory and its connection to function spaces and special functions, the heat and the wave equation. 
Len Richardson 

Harmonic analysis on homogeneous spaces; nilpotent and solvable Lie groups; representation theory; localglobal phenomena. 
Boris Rubin 

Integral geometry, harmonic analysis, fractional integration and differentiation, continuous wavelet transforms. 
Dan Sage 

Geometric and combinatorial methods in representation theory, hopf algebras and quantum groups, applications of representation theory to applied mathematics. 