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# John Toth (McGill University), Analysis Seminar

## April 26 @ 4:00 pm - 5:00 pm

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**Title: **Eigenfunction scarring and improvements in $L^{\infty}$ bounds

**Abstract:**We study the relationship between $L^\infty$ growth of eigenfunctions and their $L^2$ concentration as measured by defect measures. In particular, we show that scarring in the sense of concentration of defect measure on certain submanifolds is incompatible with maximal $L^\infty$ growth. In addition, we show that a defect measure which is too diffuse, such as the Liouville measure, is also incompatible with maximal eigenfunction growth (joint with Jeff Galkowski).