09:00 to 09:50 Registration 09:50 to 10:00 Welcome from John Toland (INI Director) INI 1 10:00 to 11:00 Bernd Ammann (Universität Regensburg)Ricci-flat manifolds and a spinorial flow Joint work with Klaus Kröncke, Hartmut Weiß and Frederik WittWe study the set of all Ricci-flat Riemannian metrics on a given compact manifold M. We say that a Ricci-flat metric on M is structured if its pullback to the universal cover admits a parallel spinor. The holonomy of these metrics is special as these manifolds carry some additional structure, e.g. a Calabi-Yau structure or a G2-structure.The set of unstructured Ricci-flat metrics is poorly understood.  Nobody knows whether unstructured compact Ricci-flat Riemannian manifolds exist, and if they exist, there is no reason to expect that the set of such metrics on a fixed compact manifold should have the structure of a smooth manifold.On the other hand, the set of structured Ricci-flat metrics on compact manifolds is now well-understood. The set of structured Ricci-flat metrics is an open and closed subset in the space of all Ricci-flat metrics. The holonomy group is constant along connected components. The dimension of the space of parallel spinors as well. The structured Ricci-flat metrics form a smooth Banach submanifold in the space of all metrics. Furthermore the associated premoduli space is a finite-dimensional smooth manifold.These results build on previous work by J. Nordström, Goto, Koiso, Tian & Todorov, Joyce, McKenzie Wang and many others. The important step is to pass from irreducible to reducible holonomy groups.In the last part of the talk we summarize work on the L2-gradient flow of the functional $(g,\phi)\mapsto E(g,\phi):=\int_M|\nabla^g\phi|^2$. This is a weakly parabolic flow on the space of metrics and spinors of constant unit length. The flow is supposed to flow against structured Ricci-flat metics. Its geometric interpretation in dimension 2 is some kind of Willmore flow, and in dimension 3 it is a frame flow.We find that the functional E is a Morse-Bott functional. This fact is related to stability questions.Associated publications:http://www.mathematik.uni-regensburg.de/ammann/preprints/holrig http://www.mathematik.uni-regensburg.de/ammann/preprints/spinorflowIhttp://www.mathematik.uni-regensburg.de/ammann/preprints/spinorflowII INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Yong Wei (University College London)Laplacian flow for closed G_2-structures We will discuss the Laplacian flow for closed G_2 structures. This flow was introduced by R. Bryant in 1992 to study the geometry of G_2 structures, inspired by Hamilton's Ricci flow in studying the generic Riemannian structures and the Kahler Ricci flow in studying Kahler structures. The primary goal is to understand the conditions under which the Laplacian flow can converge to a torsion free G_2 structures, and thus Ricci flat metric with holonomy G_2. I will start with the background of G_2 structure and the motivation of introducing the Laplacian flow, and then describe my recent progress on this flow (Joint work with Jason D. Lotay). INI 1 12:30 to 13:30 Lunch @ Wolfson Court 14:30 to 15:30 Bruno Premoselli (Université Libre de Bruxelles)Non-compactness of initial data sets in high dimensions. We will discuss instability and non-compactness results for the conformal constraint equations in dimensions larger than six. These equations are obtained from the classical constraint equations of the evolution problem in General Relativity after a conformal change of variables. The system obtained in this way is a nonlinear critical system of elliptic PDEs.We will show that in high dimensions blowing-up solutions of this system of equations naturally appear. The method is constructive, and the construction involves topological and blow-up techniques and relies on the a priori analysis of defects of compactness for critical elliptic PDEs. A reformulation in terms of the initial-value problem will be given. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Dmitri Panov (King's College London)Circle-invariant definite connections and symplectic Fano 6-manifolds The talk will be based on a joint work with Joel Fine. A definite connection on  a four manifold consists of a rank three Euclidean bundle with a metric connection whose curvature is maximally non-degenerate. I will explain why only the four sphere and the complex projective plane admit a definite connection with circle symmetry. The proof relies on properties of Hamiltonian S^1 actions on symplectic manifolds. INI 1 17:00 to 18:00 Welcome Wine Reception
 09:00 to 10:00 Oliver Schlotterer (Max-Planck-Institut für Gravitationphysik)Universality in string interactions Co-Authors: Yu-tin Huang (National Taiwan University), Congkao Wen (Tor Vergata Rome)In this talk based on arXiv:1602.01674, we provide evidence for universality in the low-energy expansion of tree-level string interactions. More precisely, in the $\alpha'$-expansion of tree-level scattering amplitudes, we conjecture that the leading transcendental coefficient at each order in $\alpha'$ is universal for all perturbative string theories. We have checked this universality up to seven points and trace its origin to the ability to restructure the disk integrals of open bosonic string into those of the superstring. The accompanying kinematic functions have the same low-energy limit and do not introduce any transcendental numbers in their $\alpha'$-corrections. Universality in the closed-string sector then follows from the Kawai-Lewellen-Tye-relations. INI 1 10:00 to 11:00 Nathan Berkovits (ICTP-SAIFR/IFT-UNESP, Sao Paulo)Untwisting the pure spinor formalism The pure spinor formalism for the superstring  is a twisted N=2 superconformal field theory where the BRST current and the b ghost are the two fermionic generators. After untwisting this N=2 superconformal field theory and defining the N=1 superconformal generator G = j_{BRST} + b, the pure spinor formalism can be described with manifest N=1 worldsheet supersymmetry. This N=1 supersymmetric description is useful for comparing with the RNS formalism and for constructing worldsheet supersymmetric sigma models for Ramond-Ramond backgrounds such as AdS_5xS^5. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Piotr Tourkine (University of Cambridge)On the null string origin of the ambitwistor string  Co-Author: Eduardo Casali (Math. Institute, Oxford) Based on: [arXiv:1606.05636]  The CHY formulae are a set of remarkable formulae describing the scattering amplitudes of a variety of massless theories, as worldsheet integrals localized on the solutions to certain polynomial equations (scattering equations). These formulae arise from a new class of holomorphic string theories called Ambitwistor strings that encode exactly the classical dynamics of the supergravity (Yang-Mills) modes of string theory. Despite some recent progress by W. Siegel and collaborators, it remained as an open question as to what extent this theory was connected to the full string theory. The most mysterious point being certainly that the localization equations of the ambitwistor string also appear in the zero tension limit of string theory (alpha’ to infinity), which is the opposite limit than the supergravity one (alpha’ to zero). In this talk, I’ll report on some work in collaboration with E. Casali and argue that the ambitwistor string is actually a tensionless string. Using some forgotten results on the quantization of these objects, we explain that the quantization of tensionless strings is ambiguous, and can lead either to a higher-spin like'' theory, or to the ambitwistor string, hence clarifying the previously mentioned paradox. In passing, we see that the degenerations of the tensile worldsheet that lead to tensionless strings make connection with Galilean Conformal Algebras and the (3d) BMS algebra. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 14:30 to 15:30 Alexander Ochirov (University of Edinburgh)Color-kinematics duality for QCD and pure gravities Color-kinematics duality has been shown to be present in QCD scattering amplitudes with massive quarks. More generally, the duality was extended to gauge theories with flavored massive matter in any Lie-algebra representation, with the resulting double copy for gravitational amplitudes. In this talk, I will discuss the details of the extension, including a new decomposition of QCD amplitudes into independent color-ordered primitives, and how the duality imposes new relations between the primitives. Furthermore, I will discuss how the extension of the duality can be used to compute gravitational amplitudes with matter and how this can be used to obtain amplitudes in pure gravity theories.Associated publications together with Henrik Johansson (Uppsala University & Nordita): http://arxiv.org/abs/arXiv:1507.00332http://arxiv.org/abs/arXiv:1407.4772 INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Jaroslav Trnka (University of California, Davis)Singularity structure of gravity amplitudes Coauthor: Enrico HerrmannThere has been a lot of progress in exploring new mathematical structures in N=4 SYM amplitudes: on-shell diagrams and Amplituhedron in the planar sector, and special properties of integrands beyond the planar limit. I will review some of these developments and then focus how the similar ideas can be extended to N=8 supergravity amplitudes. As it turns out the singularity structure of supergravity amplitudes is very different and it exhibits some surprising features at both UV and IR. INI 1