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Partial differential equations (PDE) is a many-faceted subject. Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations. Examples are sound, heat, diffusion, electrodynamics, fluid dynamics, elasticity, gravitation and quantum mechanics.

Partial differential equations also play a central role in modern mathematics, especially in geometry and analysis. It has developed into a body of material that interacts with many branches of mathematics, such as differential geometry, complex analysis, and harmonic analysis, as well as a ubiquitous factor in mathematical physics.

Our group in analysis of PDE investigates dispersive equations, wave equations, microlocal analysis, fluid mechanics and mathematical general relativity.

Calculus and the theory of real and complex continuous functions are among the crowning achievements of science. The field of mathematical analysis continues the development of that theory today to give even greater power and generality.

Some specific interests of the group members are: Complex analysis, quasi conformal mappings, fractal  geometry, Operator algebras, Elliptic PDE and nonlocal elliptic problem, Harmonic Analysis and its application to PDE, Conformal Geoemetry, Complex (quaternionic) analysis of several variables, pluripotential theory, analysis of invariant differential operators and differential complexes, geometric analysis, decoupling inequalities, eigenfunction estimates on compact Riemannian manifolds, free boundary problems, dispersive equations, microlocal analysis with applications to differential geometry and mathematical physics (index theory).