Pedram Hekmati

Moduli spaces of contact instantons

Abstract We construct the moduli space of contact instantons, an analogue of Yang–Mills instantons defined for contact metric 5-manifolds and initiate the study of their structure. In the K-contact case we give sufficient conditions for smoothness of the moduli space away from reducible connections and show the dimension is given by the index of an operator elliptic transverse to the Reeb foliation. The moduli spaces are shown to be Kahler when the 5-manifold M is Sasakian and hyperKahler when M is transverse Calabi–Yau. We show how the transverse index can be computed in various cases, in particular we compute the index for the toric Sasaki–Einstein spaces Y p , q .

The general caloron correspondence

Abstract We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal G -bundle Q over a manifold X , including the case of the gauge group of Q . These results are used to define characteristic classes of gauge group bundles. Explicit but complicated differential form representatives are computed in terms of a connection and Higgs field.

A geometric model for odd differential K-theory☆

Odd K-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential K-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons–Sullivan construction of even differential K-theory. We use this model to prove a conjecture of Tradler–Wilson–Zeinalian [16], which states that the model developed there also defines the unique differential extension of odd K-theory.

Calculus structure on the Lie conformal algebra complex and the variational complex

We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [A. De Sole and V. G. Kac, ...

Integrability criterion for abelian extensions of Lie groups

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension , where is connected, simply connected and for some discrete subgroup . When , the kernel is replaced by a central extension of by .

Arithmetic of singular character varieties and their E-polynomials

We calculate the E-polynomials of the SL3(C)- and GL3(C)-character varieties of compact oriented surfaces of any genus and the E-polynomials of the SL2(C)- and GL2(C)-character varieties of compact non-orientable surfaces of any Euler characteristic. Our methods also give a new and significantly simpler computation of the E-polynomials of the SL2(C)-character varieties of compact orientable surfaces, which were computed by Logares, Munoz and Newstead for genus g=1,2 and by Martinez and Munoz for g⩾3. Our technique is based on the arithmetic of character varieties over finite fields. More specifically, we show how to extend the approach of Hausel and Rodriguez-Villegas used for non-singular (twisted) character varieties to the singular (untwisted) case.

The Faddeev–Mickelsson–Shatashvili Anomaly and Lifting Bundle Gerbes

In gauge theory, the Faddeev–Mickelsson–Shatashvili anomaly arises as a prolongation problem for the action of the gauge group on a bundle of projective Fock spaces. In this paper, we study this anomaly from the point of view of bundle gerbes and give several equivalent descriptions of the obstruction. These include lifting bundle gerbes with non-trivial structure group bundle and bundle gerbes related to the caloron correspondence.

Projective families of Dirac operators on a Banach Lie groupoid

We introduce a Banach Lie group

A Fourier-Mukai approach to the K-theory of compact Lie groups

G

Transitive Courant algebroids, string structures and T-duality

of unitary operators subject to a natural trace condition. We compute the homotopy groups of