Which magnetic fields support a zero mode?

Abstract: Motivated by the question from mathematical physics about the size of magnetic fields that support zero modes for the three dimensional Dirac equation, we study a certain conformally invariant spinor equation. We state some conjectures and present some results supporting them. Those concern, in particular, two novel Sobolev inequalities for spinors and vector fields.

The talk is based on joint work with Michael Loss.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

( video )

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

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