BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Regularized index of non-Fredholm Dirac-Schrödinger operators
DTSTART:20241203T131500Z
DTEND:20241203T141500Z
DTSTAMP:20260305T175400Z
UID:indico-event-116@math-events.uni-bonn.de
DESCRIPTION:Speakers: Oliver Fürst (Uni Bonn)\n\nA Dirac-Schrödinger ope
 rator is a Dirac operator over a non-compact manifold M perturbed by an o
 perator valued potential A\, acting pointwise in a Hilbert space H. The po
 tential A admits decay of its derivative in some sense\, and it is usuall
 y required that A is invertible outside some compact region\, allowing th
 e operator D to be Fredholm. The Fredholm index problem of D is well stud
 ied\, and there exists an abundance of associated index theorems\, the mo
 st famous of which might be one of its earliest incarnations\, the ”ind
 ex=spectral flow”-theorem.In this talk\, the invertibility condition on 
 A is suspended\, and therefore D will not be Fredholm. However\, there exi
 sts a notion of regularized index via trace limits (the so-called Witten i
 ndex)\, which we will apply here. We will see that a general trace formula
  leads to a new index formula\, which we will investigate in the example o
 f the (d + 1)-massless Dirac-Schrödinger operators in Rd+1. In particular
 \, we show that its Witten index may attain any real number\, in stark con
 trast to the Fredholm index.\n\nhttps://math-events.uni-bonn.de/event/116
 /
LOCATION:Seminar room 0.008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/116/
END:VEVENT
END:VCALENDAR