The research activities of the Mathematics Analysis Group focus on:
- Construction of class of representations of discrete hyperbolic fundamental groups of surfaces.
- Construction of mathematical transforms defined in the spectral domain of finite graphs and applications to compression, denoising and reconstruction of signals defined on large graphs.
- Comparison results for solutions to boundary value problems for nonlinear elliptic and parabolic partial differential equations
- Nonstandard symmetrization methods and symmetry results for nonlinear elliptic equations
- Existence, uniqueness and regularity of solutions to nonlinear elliptic and parabolic partial differential equations with data affected by low degree of integrability
- Functional inequalities and their applications to PDEs