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• #### Getzler rescaling via adiabatic deformation and a renormalized local index formula ﻿

[OWP-2016-18] (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)
We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). After introducing a renormalized supertrace on Lie manifolds with spin ...
• #### Real group orbits on flag ind-varieties of SL (∞, C) ﻿

[OWP-2016-01] (Mathematisches Forschungsinstitut Oberwolfach, 2016-05-10)
We consider the complex ind-group $G=SL (\infty, \mathbb{C})$ and its real forms $G^0=SU(\infty,\infty)$, $SU(p,\infty)$, $SL(\infty,\mathbb{R})$, $SL(\infty,\mathbb{H})$. Our main object of study are the $G^0$-orbits on ...