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14 Febbraio, 2025 11:00
Sezione di Analisi

Estimates on the nodal sets of solutions to Dirac equations

Ruijun WU, Beijing Institute of Technology
Aula Seminari - III Piano
Abstract

Motivated by the various Dirac equations in geometry and physics, we consider the nodal set of solutions to a class of Dirac equations. In contrast to scalar function case, we show that the nodal sets in general has codimension at least two, which strengthen the known results in the smooth setting and confirms a conjecture in spin geometry.
Moreover, using a spinorial version of the frequency function, we show that the nodal set can be stratified nicely.
This is based on a joint work with A. Malchiodi and W. Borrelli.