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SUMMARY:Mihajlo Cekić (Université Paris-Saclay)
DTSTART:20210923T160000Z
DTEND:20210923T170000Z
DTSTAMP:20260423T021224Z
UID:Inverse/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/58/"
 >The Holonomy Inverse Problem</a>\nby Mihajlo Cekić (Université Paris-Sa
 clay) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n
 \n\nAbstract\nGiven a compact Riemannian manifold (M\, g) and a vector bun
 dle over M equipped with a connection\, we consider the following question
 : does the holonomy along closed geodesics determine the gauge (equivalenc
 e) class of the connection? If (M\, g) has negative curvature or more gene
 rally its geodesic flow is Anosov\, in this talk I will explain how in fac
 t\, only the traces of the holonomy along closed geodesics locally determi
 ne a generic connection\; global uniqueness results are obtained in some c
 ases. A direct consequence is an inverse spectral result for the connectio
 n (magnetic) Laplacian. The proof relies on two new ingredients: a Livšic
  type theorem in hyperbolic dynamics for unitary cocycles\, and the interp
 lay between the local geometry of the moduli space of connections with Pol
 licott-Ruelle resonances of a certain natural transport operator. Joint wo
 rk with Thibault Lefeuvre.\n
LOCATION:https://researchseminars.org/talk/Inverse/58/
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