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SUMMARY:Matteo Capoferri (Cardiff University)
DTSTART:20200528T100000Z
DTEND:20200528T105000Z
DTSTAMP:20260416T065420Z
UID:IML-SMR/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML-SMR/4/">
 Global propagator for the massless Dirac operator and spectral asymptotics
 </a>\nby Matteo Capoferri (Cardiff University) as part of Scattering\, mic
 rolocal analysis and renormalisation\n\n\nAbstract\nWe construct the propa
 gator of the massless Dirac operator W on a closed Riemannian 3-manifold a
 s the sum of two invariantly defined oscillatory integrals\, global in spa
 ce and in time\, with distinguished complex-valued phase functions. The tw
 o oscillatory integrals – the positive and the negative propagators – 
 correspond to positive and negative eigenvalues of W\, respectively. This 
 enables us to provide a global invariant definition of the full symbols of
  the propagators (scalar matrix-functions on the cotangent bundle)\, a clo
 sed formula for the principal symbols and an algorithm for the explicit ca
 lculation of all their homogeneous components. Furthermore\, we obtain sma
 ll time expansions for principal and subprincipal symbols of the propagato
 rs in terms of geometric invariants. Lastly\, we use our results to comput
 e the third local Weyl coefficients in the asymptotic expansion of the eig
 envalue counting functions of W.\n
LOCATION:https://researchseminars.org/talk/IML-SMR/4/
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