Talks

The distinction between a realist interpretation of quantum theory that is psi-ontic and one that is psi-epistemic is whether or not a difference in the quantum state necessarily implies a difference in the underlying ontic state. Psi-ontologists believe that it does, psi-epistemicists that it does not. This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position. The first assumption of the theorem - that holistic properties may exist for composite systems, but do not arise for unentangled quantum states - is only appealing if one is already predisposed to a psi-ontic view. The more natural assumption of separability (no holistic properties) coupled with the other assumptions of the theorem rules out both psi-ontic and psi-epistemic models and so does not decide between them. The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario.

It is well known that on-shell recursion relation can be applied to tree-level amplitude in string theory. One technical issue of the application is the sum of infinite middle on-shell states. We discuss how we can do the sum exactly to reproduce the known result.

With the emergence of the dark sector in cosmology,  a variety of modified theories of gravity have come to the fore. I will discuss a framework which can be used to test gravity on large scales and the observational programmes that might lead to the tightest constraints.

In this talk I will review recent results we obtained regarding the computation of Wilson loops in the context of the AdS/CFT correspondence. According to such correspondence Wilson loops are related to minimal area surfaces in hyperbolic space. The problem reduces to solving a set of non-linear but integrable differential equations. The solutions can be expressed in terms of Riemann theta functions. Other methods such as the dressing method applied to this problem will also be discussed.

I will outline a couple of constructions of co-Higgs bundles, which are holomorphic vector bundles with Higgs fields taking values in the tangent bundle. One reason why these objects are interesting is that they are precisely the generalized holomorphic bundles on an ordinary complex manifold considered as a generalized complex manifold. One method produces a co-Higgs bundle on any complex manifold; in a sense, this is the canonical co-Higgs bundle. The other is specifically for the projective plane. Recall that one of the earliest constructions of (interesting) vector bundles
on a complex surface was Schwarzenberger's construction of a rank-2 vector bundle on the projective plane from a double cover. I hope to breathe new life into this object by showing that the bundle carries a natural O(1)-valued Higgs field, which can be pushed to a T-valued Higgs field on P2. For both examples, we will discuss some aspects of their stability and deformation theory.

Matrix models yield a theory of random two dimensional surfaces. They support a 1/N expansion dominated by planar graphs (corresponding to planar surfaces) and undergo a phase transition to a continuum theory. In higher dimensions matrix models generalize to tensor models. In the absence of a viable 1=N expansion, tensor models have for a long time been less successful in providing a theory of random higher dimensional spaces. This situation has drastically changed recently. Models for a non-symmetric complex tensor have been shown to admit a 1/N expansion dominated by graphs of spherical topology in arbitrary dimensions and to undergo a phase transition to a continuum theory. I will present an overview of these results and discuss their implications.

This talk will give a survey of some recent developments on the construction and classification of compact manifolds with holonomy G2 and their calibrated submanifolds. After reviewing previous work we concentrate on the following three developments: (a) the construction of many new compact G2 manifolds using weak Fano 3-folds; (b) the construction of many compact G2 manifolds containing rigid associative 3-folds; (c) the diffeomorphism classification of (2-connected) G2 manifolds obtained by twisted connect sums. If time permits we will mention new questions
suggested by our results. This work is joint with Alessio Corti, Johannes Nordstrom, and Tommaso Pacini.

In this talk, I will discuss my recent works with J. Streets on curvature ows on Hermitian manifolds and show how they can be used to study generalized Kahler manifolds. I will also show how they are related to the renormalization group ow coupled with B- elds. Some open problems will be discussed. In the end, I will also discuss briey a new ow which preserves symplectic structures.

Asymptotically conical (AC) Calabi-Yau manifolds are Ricci-at Kahler manifolds that resemble a Ricci-at Kahler cone at infinity. I will describe an existence theorem for AC Calabi-Yau manifolds which, in particular, yields a refinement of an existence theorem of Tian and Yau for such manifolds. I will also discuss some examples. This is ongoing work with Hans-Joachim Hein.

I will discuss some joint work with K. Uhlenbeck. There is a general method for constructing soliton hierarchies from a splitting of Lie algebras. We explain how formal scattering and inverse scattering, Hamiltonian structures, commuting conservation laws, Backlund transformations, tau functions, and Virasoro actions on tau functions can all be constructed in a uni ed way from such splittings.