Uppsala

We shall consider a crossing equation of the Euclidean conformal group in terms of conformal partial waves and in particular, a position independent representation of this equation. We shall briefly discuss the relevance of this equation to the problem of cosmological bootstrap. Thereafter, we shall sketch the derivation of the Biedenharn-Eliiot identity (a pentagon identity) for the 6j symbols of the conformal group and show how this provides us with an exact solution to said crossing equation. For the conformal group (which is non-compact), this involves some careful bookkeeping of the spinning representations. Finally, we shall discuss some consistency checks on the result obtained, and some open questions. 

G2 structure manifolds are a key ingredient in supersymmetric compactifications on seven-manifolds. We will discuss the fact that G2 structure manifolds admit refinements in the form of almost contact (3-) structures.  In fact, there are infinite dimensional spaces of these structures. We will discuss topological and differential geometric aspects of (the space of) these refinements. We will then explore applications in physics, including supersymmetry enhancement. This is based on 2101.12605.

Manifolds with G2 structure allow almost contact structures. In this talk I will discuss various aspects of such structures, and their effect on certain supersymmetric configurations in string and M-theory.

This is based on recent work with Xenia de la Ossa and Matthew Magill.

In this talk, I will describe new mathematical structures in the low-energy  expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited  to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic  Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string  low-energy expansions.
 

In this talk, we show that a range of non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Among the possible SU(3) structures we find Strominger-Hull systems, suitable for heterotic or type II string compactifications. These SU(3) structures of Strominger-Hull type have a non-vanishing and non-closed three-form flux which needs to be supported by source terms in the associated Bianchi identity. We discuss the possibility of finding such source terms and present first steps towards their explicit construction. Provided suitable sources exist, our methods lead to Calabi-Yau compactifications of string theory with a non Ricci-flat, physical metric which can be written down explicitly and in analytic form. The talk is based on the paper 1805.08499.

We show how to compute the symplectic homology of a 4-dimensional Weinstein manifold from a diagram of the Legendrian link which is the attaching locus of its 2-handles. The computation uses a combination of a generalization of Chekanov's description of the Legendrian homology of links in standard contact 3-space, where the ambient contact manifold is replaced by a connected sum of $S^1\times S^2$'s, and recent results on the behaviour of holomorphic curve invariants under Legendrian surgery.