Related papers: Two nontrivial index theorems in odd dimensions

Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, a bordism invariant of string manifolds in dimensions $4m-1$. We prove a secondary index theorem which relates this global-analytic…

We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…

We prove inverse theorems for the size of sumsets and the $L^q$ norms of convolutions in the discretized setting, extending to arbitrary dimension an earlier result of the author in the line. These results have applications to the…

We discuss two variations of Edwards' duality theorem. More precisely, we prove one version of the theorem for cones not necessarily containing all constant functions. In particular, we allow the functions in the cone to have a non-empty…

Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.

We formulate two types of extension of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval…

In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation $\varphi $ of a d-dimensional $(d \ge 2)$ Euclidean…

Nonrenormalization theorems involving the transverse, i.e. non anomalous, part of the <VVA> correlator in perturbative QCD are proven. Some of their consequences and questions they raise are discussed.

We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set…

In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…

We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new…

We study two families of $g$-dimensional abelian varieties, induced by distinct rational maps defined on a common variety $\overline{\mathcal A}$ and mapping to two bases $\overline{S}_1$ and $\overline{S}_2$. Two non-torsion sections…

The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the…

In [19], a general Dabrowski-Sitarz-Zalecki type theorem for odd dimensional manifolds with boundary was proved. In this paper, we give the proof of the another general Dabrowski-Sitarz-Zalecki type theorem for the spectral Einstein…

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold.…

We generalize Turaev's definition of torsion invariants of pairs (M,x), where M is a 3-dimensional manifold and x is an Euler structure on M (a non-singular vector field up to homotopy relative to bM and local modifications in int(M).…

We prove new results on the additive theory of reversed primes $\overleftarrow{p}$; that is, primes $p$ which are written backwards in a fixed base $b\geq 2$. In particular, we study a variant of Goldbach's conjecture, looking at…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

These notes are based on lectures on index theory, topology, and operator algebras at the "School on High Dimensional Manifold Theory" at the ICTP in Trieste, and at the Seminari di Geometria 2002 in Bologna. We describe how techniques…

We study elliptic theory on manifolds with boundary represented as a covering space. Firstly, we consider boundary value problems, where the boundary conditions are allowed to mix the values of functions in the fibers of the covering. We…