scnews: "Asia-Pacific Analysis and PDE Seminar: Joachim Kerner -- Some Comments on the spectral gap" by Miranda Luo

Dear friends and colleagues,

on Monday, 13 June 2022 at
• 02:00 PM for Beijing, Hong Kong and Perth
• 03:00 PM for Seoul and Tokyo
• 04:00 PM for Canberra, Melbourne and Sydney
• 06:00 PM for Auckland

Professor Joachim Kerner is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Some Comments on the spectral gap

Abstract:

In this talk we shall discuss recent results on the spectral gap of Schrödinger operators in one and higher dimensions. In particular, we are interested in understanding the effect of an external potential on the spectral gap (which is defined as the difference between the first two eigenvalues) in a limit where the volume of the underlying domain tends to infinity. In this limit, we aim at establishing upper and lower bounds on the spectral gap for a rather large class of potentials. Quite surprisingly, in doing so, we come across an interesting phenomenon: namely, in the one-dimensional setting, it turns out that even compactly supported potentials are enough to drastically alter the asymptotic behaviour of the spectral gap. As we shall see, this is due to an effective degeneracy of the ground state in the infinite-volume limit. In higher dimensions, this effect disappears for compactly supported potentials but, by looking at different potentials, it may nevertheless be recovered.

This talk is based on joint work with Matthias Täufer (University of Hagen, Germany).

Chair: Daniel Hauer (University of Sydney, Australia)

More information and how to attend this talk can be found at the seminar webpage .

Miranda
On behalf of Daniel H. and Ben

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Webinar Speaker

Joachim Kerner

Professor @University of Wuppertal, Germany

Professor Kerner received his PhD from the University of London (Royal Holloway, United Kingdom) in the year 2013 under supervision of Professor Jens Bolte. After a few months as a postdoc at the Universität Stuttgart (Germany), he joined the University of Hagen (Germany) in 2014 as a postdoctoral research fellow. In 2020, Kerner got promoted as Senior Lecturer at the University of Hagen (non-permanent). In 2016, he received a faculty prize for an outstanding publication. Professor Kerner is currently as a substitute professor at the Bergische Universität in Wuppertal (while on leave from the University of Hagen).

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