Analysis

The research carried out by the members of the Analysis Group, primarily focused on partial differential equations and related areas, covers a wide range of topics, from classical aspects of PDEs, to microlocal and global analysis, analysis on graphs, spectral theory, nonlinear equations, and complex analysis in several variables.

Faculty

Shif Berhanu's research interests lie in the areas of partial differential equations and complex analysis. He has worked on the qualitative and boundary properties of complex vector fields. His current interests include Vekua-type equations and the analytic regularity of solutions of fully nonlinear first order partial differential equations

Cristian Gutierrez's research interests are in the areas of partial differential equations and harmonic analysis. He has worked on weighted norm inequalities, singular integrals, Hardy spaces, Gaussian harmonic analysis, parabolic equations, subelliptic equations, and nonlinear elliptic equations. His current research interests include geometric optics and nonlinear PDEs of Monge-Ampere type.

Gerardo Mendoza's main area of research is linear partial differential equations. He has done work in microlocal analysis, solvability, complex analysis, and analysis on manifolds with singularities. His current interests lie in global analysis, principally on manifolds with singularities, spectral theory of partial differential operators on such manifolds, and various aspects of elliptic differential complexes ranging from local to global.

Irina Mitrea's research interests are in the areas of harmonic analysis, partial differential equations, geometric measure theory, and scattering theory. Her work has been motivated by the study of well-posedness of boundary value problems for elliptic equations and systems of second and higher order in domains with irregular boundaries. Mitrea's current research interests include analysis on quasi-metric spaces and applications of harmonic analysis tools to several complex variables.

Isaac Pesenson is interested in Shannon sampling, wavelets and frames on manifolds, Heisenberg-type groups and quantum and combinatorial graphs. He is currently working on developing time-frequency analysis on manifolds and graphs and its applications to CMB, high-dimensional data dimension reduction, image processing, visualization and learning theory.

Research Profile

The Analysis group is active in a variety of research areas including:

Seminars

Graduate Studies in Analysis

Several graduate students have completed Ph.D.s in analysis in recent years. Interested graduate students are encouraged to take advanced topics courses in these and related areas and to attend the above listed weekly seminars.

General information about graduate study in mathematics at Temple, including course descriptions, can be found on the graduate program website.

Selected Courses