This overview is based on the talk [101] given at the mini-workshop 0648c" Dirac operators
in di? erential and non-commutative geometry", Mat-matisches Forschungsinstitut …

Motivated by SU (3) structure compactifications, we show explicitly how to construct half-flat
topological mirrors to Calabi-Yau manifolds with NS fluxes. Units of flux are exchanged with …

We prove existence results for Dirac-harmonic maps using index theoretical tools. They are
mainly interesting if the source manifold has dimension 1 or 2 modulo 8. Our solutions are …

Let M be a compact spin manifold with a chosen spin structure. The Atiyah–Singer index
theorem implies that for any Riemannian metric on M the dimension of the kernel of the …

Prescribing eigenvalues of the Dirac operator Page 1 manuscripta math. 118, 191–199 (2005)
© Springer-Verlag 2005 Mattias Dahl Prescribing eigenvalues of the Dirac operator Received …

Mathematische Annalen Page 1 Math. Ann. (2008) 340:1–21 DOI 10.1007/s00208-007-0137-8
Mathematische Annalen Weyl laws on open manifolds Sergiu Moroianu Received: 14 …

In this paper, we estimate the supremum of Perelman's λ-functional λ M (g) on Riemannian 4-
manifold (M, g) by using the Seiberg-Witten equations. Among other things, we prove that …

We introduce a differential topological invariant for compact differentiable manifolds by
counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if …

We construct a class of symplectic non-Kähler and complex non-Kähler string theory vacua,
extending and providing evidence for an earlier suggestion by Polchinski and Strominger …

Let M be a compact manifold with a spin structure χ and a Riemannian metric g. Let λg2 be
the smallest eigenvalue of the square of the Dirac operator with respect to g and χ. The τ …