Research Areas

• Signal detection, spike sorting and time series analysis of multi-dimensional neurobehavioral measurements

• Multiple hypothesis testing in large scale, higher criticism and their applications in signal detection in noisy time series and density estimation

• Heat kernel expansions on curved geometries and their applications in financial mathematics and geometric dimension reduction

• Applications of stochastic analysis, Feynman-Kac formula and combinatorial structures in heat kernel expansions on curved geometries

• Noncommutative differential and spectral geometry

• Local geometric invariants of noncommutative tori

• Arithmetic structures in the heat kenrel expansion of the Dirac-Laplacian of cosmological models

• Noncommutative residues on algebras of pseudodifferential operators and their applications to heat expansion on curved geometries