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Analysis and Partial Differential Equations

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More about this group

The analysis group researches the qualitative and quantitative theory of parabolic and elliptic partial differential equations (PDEs), spectral theory, stochastic analysis and the theory of function spaces.

Physically, parabolic PDEs describe the diffusion of heat in different materials at varying temperature points over time. Elliptic PDEs occur in the study of stationary solutions of heat flow problems and, in the case of the Schrodinger equation, bound and scattering states in quantum mechanics.

The theory of elliptic and parabolic PDEs is multidisciplinary, linking aspects of stochastic analysis, functional analysis and potential theory with geometry and topology.

The mathematicians Gordon, Webb, Wolpert proved that you cannot deduct the shape of a drum from the frequency of sound it emits. However, there are geometrics you can construct from the frequency, for example, the volume or the perimeter.