Analysis & PDE
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Analysis & PDE

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.

 

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.