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SUMMARY:Francesco Bei (Università di Roma La Sapienza)
DTSTART:20201210T133000Z
DTEND:20201210T143000Z
DTSTAMP:20260423T024519Z
UID:GeoSem/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GeoSem/9/">O
 n the spectral theory and analytic K-homology of complex spaces</a>\nby Fr
 ancesco Bei (Università di Roma La Sapienza) as part of Geometry Seminar 
 - University of Florence\n\n\nAbstract\nLet $(X\, h)$ be a compact and irr
 educible Hermitian complex space. In the last\nthirty years\, motivated am
 ong other things by the Cheeger-Goresky-MacPherson\nconjecture and the Rie
 mann-Roch theorem of Baum-Fulton-MacPherson\, the $L^2$-\ntheory of the Ho
 dge-de Rham operator $d + d^t$\, the Hodge-Dolbeault operator $\\overline\
 \partial + \\overline\\partial^t$ and the associated Laplacians on $(X\, h
 )$ has been the subject of many investigations. In the first part of this 
 talk we will report about some recent results concerning the existence of 
 self-adjoint extensions of the Hodge-\nKodaira Laplacian with entirely dis
 crete spectrum. Then in the second part we will describe some applications
  to the K-homology of X. In particular assuming $\\dim(sing(X)) = 0$ we wi
 ll show how the operator $\\overline\\partial+\\overline\\partial^t$ induc
 es an analytic K-homology class in $K^{an}_{0}(X)$ and we will give a geom
 etric interpretation of this class in terms of a resolution of $X$.\n
LOCATION:https://researchseminars.org/talk/GeoSem/9/
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