Twistor Theory and Beyond

Contribution List

1. Rod Gover -- A conformally invariant Yang-Mills energy and equation on 6-manifolds

27/09/2021, 10:00

A conformally invariant Yang-Mills energy and equation on 6-manifolds. The gauge field equations known as the Yang-Mills equations are extremely important in both mathematics and physics, and their conformal invariance in dimension 4 is a critical feature for many applications. In dimension 4, and when specialised to the Cartan/tractor connection, the Yang-Mills current recovers exactly the...

2. David Skinner -- Twistors, Integrability and 4d Chern-Simons Theory

27/09/2021, 11:30

Costello, Witten & Yamazaki have recently introduced a new approach to 2d integrable systems based on a variant of Chern-Simons theory living in 4d. I’ll review this story, and show how it is deeply connected both to Lionel’s work on the twistor construction of integrable systems, and to his more recent work on scattering amplitudes in four dimensional gauge theories.

3. Nathan Berkovits -- Twistors and the AdS_5 x S^5 Superstring

27/09/2021, 14:00

I will describe recent approaches to including twistors in the worldsheet description of the superstring in an AdS_5 x S^5 background.

4. Claude LeBrun -- Einstein Manifolds, Conformal Curvature, and Anti-Holomorphic Involutions

27/09/2021, 15:30

5. Anastasia Volovich -- Recent Developments in N=4 Yang-Mills Amplitudes.

27/09/2021, 16:30

6. Prim Plansangkate -- Einstein-Weyl structures and dispersionless equations

28/09/2021, 10:00

We shall demonstrate via a simple transformation that, under symmetry assumption, the equations governing a general anti-self-dual conformal structure in four dimensions can be explicitly reduced to the Manakov-Santini system, which determines the three-dimensional Einstein-Weyl structure on the space of orbits of symmetry. Then we move on to discuss the mn-dKP equation, which is a...

7. Jerzy Lewandowski -- Spacetime, structures, equations and solutions

28/09/2021, 11:30

When I met Lionel at Syracuse in the winter of 1991, he was interested in null structures, the spacetimes that admit them and the equations they may satisfy. Some of these, along with a few others and new results, will be discussed in this lecture.

For curved spacetime, the twistor equation relates the local twistor connection to the Chern-Moser connection of the CR structure and the...

8. Ian Strachan -- Twistor Theory and Donaldson-Thomas Invariants

28/09/2021, 14:00

Lionel taught us how to use the Lie algebra of volume preserving diffeomorphism of a surface in Lax pairs, thus making the connection between integrable systems and curved twistor spaces. He also taught us how isomonodromy problems have a natural twistorial interpretation. In this talk it is shown how the wall-crossing phenomena in the theory of Donaldson-Thomas invariants results in a...

9. Jaroslav Trnka -- Negative Amplituhedron Geometries and Amplitudes at Strong Coupling

28/09/2021, 15:30

We define negative Amplituhedron geometries which generalize the Amplituhedron picture for scattering amplitudes in planar N=4 SYM theory. We show that these geometries naturally describe the logarithm of the amplitude, and we use them to define a certain IR finite object as the dlog form on negative geometries. In certain limits, we determine this object to all loop orders, perform...

10. Lance Dixon -- Surveying the Mason-Dixon Line

28/09/2021, 16:30

I recount some of my cherished overlaps and interactions with Lionel, both linear and nonlinear, over the past 16 years, as we have pursued complementary approaches to understanding what amplitudes are.

11. Yvonne Geyer -- Loop integrands from the Ambitwistor String

29/09/2021, 10:00

In this talk, I will present an overview of the Ambitwistor String, a class of worldsheet models describing field theory, with particular focus on the progress in understanding loop amplitudes in Yang-Mills theory and gravity. While the worldsheet model naturally represents these amplitudes as correlators on higher genus Riemann surfaces, a residue theorem on the moduli space relates the...

12. Paul Tod -- One-sided type-D vacuum metrics are integrable

29/09/2021, 11:30

I show that any 4-dimensional Riemannian Ricci-flat metric for which either the SD or the ASD Weyl spinor is type-D has a symmetry and is determined by a solution of the Toda field equation. As a corollary, if there is a second symmetry commuting with the first then the metric is determined by an axisymmetric solution of the flat 3-dimensional Laplacian.

13. Eduardo Casali -- Threading the history of twistors with strings

29/09/2021, 14:00

I will present a review of the various successes obtained by combining twistors (and ambitwistors) with string theory, from the seminal work of Witten almost twenty years ago to recent developments in flat space holography.

14. George Sparling -- The relation between string theory, twistor theory and gravity: the past and present

29/09/2021, 15:30

Lionel Mason and his cohorts have pioneered the twistor string theory of Einstein’s gravity, based on an intense study of the propagation of gravity in null directions. I will discuss this work, invoking the spirits of the ancestors, particularly those associated with my former college, Isaac Newton, Subrahmanyan Chandrasekhar, Hermann Bondi and Jeffrey Goldstone.

15. Zvi Bern -- From Twistor Theory to Gravitational Waves

29/09/2021, 16:30

I will start with a few anecdotes about twistor theory making comments on supergravity before turning to current problems in gravitational wave physics.

16. Lionel Mason -- Overview

29/09/2021, 17:30