The cohomology groups
The eta invariant and metrics of positive scalar curvature.
The even Clifford structure of the fourth Severi variety
TheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl0(E) → End(TM) mapping Ʌ2E into skew-symmetric endomorphisms, and the existence of a metric connection on E compatible with φ. We give an explicit description of such a vector bundle E as a sub-bundle of End(TM)....
The generalized Lichnerowicz formula and analysis of Dirac operators.
The Hijazi inequalities on complete Riemannian manifolds.
The laplacian and the Dirac operator in infinitely many variables
The Srní lectures on non-integrable geometries with torsion
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...
The torsion of spinor connections and related structures.
The variational principle for the uniform acceleration and quasi-spin in two dimensional space-time.
Two new estimates for eigenvalues of Dirac operators
We establish lower and upper eigenvalue estimates for Dirac operators in different settings, a new Kirchberg type estimate for the first eigenvalue of the Dirac operator on a compact Kähler spin manifold in terms of the energy momentum tensor, and an upper bound for the smallest eigenvalues of the twisted Dirac operator on Legendrian submanifolds of Sasakian manifolds. The sharpness of those estimates is also discussed.