# Aktuelles

## Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Gregory Berkolaiko am 24.03.2021 - 17:00 Uhr im Rahmen des Forschungsseminars Analysis

[24.03.2021]

Achtung neu: Der Vortrag findet erst um 17:00 Uhr statt!

Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 24. März 2021, um 17:00 Uhr,

Herr Prof. Dr. Gregory Berkolaiko (Texas A&M University)

einen Vortrag zum Thema

Lateral variation principle and extrema of dispersion relation of periodic graphs.

Der Vortrag findet im Rahmen eines Zoom-Meetings statt:

https://fernuni-hagen.zoom.us/j/85219043827?pwd=eldtMXY2Uzk0ek1XVlo3c0lEcmUzQT09

Meeting ID: 852 1904 3827
Passcode: 93571026

Abstract: The first step in the proofs of several spectral geometry theorems is perturbing the operator "along" a given eigenfunction $f$, i.e. adding a perturbation $P$ that vanishes on $f$ and therefore leaves the corresponding eigenvalue $\lambda_0$ in its place.

But such perturbation may still affect the sequential number of $\lambda_0$ in the spectrum, creating a spectral shift. We will discuss a general theorem that recovers the value of the spectral shift by looking at the stability of $\lambda_0$ with respect to small variations of the perturbation $P$.

As an application of this result, we show that a large family of tight-binding models have a curious property: there is a local condition akin to second derivative test that detects if a critical point is a global (sic!) extremum. With some additional assumptions (time-reversal invariance and dimension 3 or less), we show that any local extremum of a given sheet of the dispersion relation is in fact the global extremum.

Based on joint work with Y. Canzani, G. Cox, P. Kuchment and J. Marzuola.

mathinf.webteam | 12.08.2021