L3

Atomistic Molecular Dynamics is a well established biomolecular modelling tool that uses the wealth of information available in the Protein Data Bank (PDB). However, biophysical techniques that provide structural information at the mesoscale, such as cryo-electron microscopy and 3D tomography, are now sufficiently mature that they merit their own online repository called the EMDataBank (EMDB). We have developed a continuum mechanics description of proteins which uses this new experimental data as input to the simulations, and which we are developing into a software tool for use by the biomolecular science community. The model is a Finite Element algorithm which we have generalised to include the thermal fluctuations that drive protein conformational changes, and which is therefore known as Fluctuating Finite Element Analysis (FFEA) [1].

We will explain the physical principles underlying FFEA and provide a practical overview of how a typical FFEA simulation is set up and executed. We will then demonstrate how FFEA can be used to model flexible biomolecular complexes from EM and other structural data using our simulations of the molecular motors and protein self-assembly as illustrative examples. We then speculate how FFEA might be integrated with atomistic models to provide a multi-scale description of biomolecular structure and dynamics.

1. Oliver R., Read D. J., Harlen O. G. & Harris S. A. “A Stochastic finite element model for the dynamics of globular macromolecules”, (2013) J. Comp. Phys. 239, 147-165.

This is will be a progress report on our long-ongoing joint work with Bezrukavnikov on lifting the monodromy of the quantum differential equation for symplectic resolutions to automorphisms of their derived categories of coherent sheaves. I will attempt to define the ingredient that go both into the problem and into its solution.
 

Following an idea of Gaiotto, a symplectic representation of a complex Lie group G defines a complex Lagrangian subvariety inside the moduli space of G-Higgs bundles. The talk will discuss the case of G=SL(2) and its link with determinant  divisors, or equivalently Brill-Noether loci, in the moduli space of semistable SL(2)-bundles. 

Given a (-1)-shifted symplectic derived scheme or stack (X,w) over C equipped with an orientation, we explain how to construct a perverse sheaf P on the classical truncation of X so that its hypercohomology H*(P) can be regarded as a categorification of (or linearisation of) X. Given also a Lagrangian morphism L -> X equipped with a relative orientation, we outline a programme in progress to construct a natural morphism of constructible complexes on the truncation of L from the (shifted) constant complex on L to a suitable pullback of P to L. The morphisms and resulting hypercohomology classes are expected to satisfy various identities under products, composition of Lagrangian correspondences, etc. This programme will have interesting applications, such as proving associativity of a Kontsevich-Soibelman type COHA multiplication on H*(P) when X is the derived moduli stack of coherent sheaves on a Calabi-Yau 3-fold Y, and defining Lagrangian Floer cohomology and the Fukaya cat!
 egory of an algebraic or complex symplectic manifold S.

Generalised Geometry is a very powerful tool to study gravity duals of strongly coupled gauge theories. In this talk I will discuss how Exceptional Geometry can be used to study marginal deformations of N=1 SCFT's in 4 and 3 dimensions.

Heterotic vacua, defined with a holomorphic bundle and connection satisfying hermitian Yang-Mills, realise four-dimensional chiral gauge theories. We exploit the rich interplay between four-dimensional physics, supersymmetry and  geometry to construct a natural Kaehler metric for the moduli space, with a shockingly simple Kaehler potential. Along the way, we discover a natural geometric structure for the heterotic moduli.
 

Recently, there has been some progress in examining mirror symmetry beyond Calabi-Yau threefolds. I will discuss how this is related to flux vacua of type II supergravity on eight-dimensional manifolds equipped with SU(4)-structure. It will be shown that the natural framework to describe such vacua is generalized complex geometry. Two classes of type IIB solutions will be given, one of which is complex, the other symplectic, and I will describe in what sense these are mirror to one another.  

The black hole information paradox comes about because of the classical no-hair theorems for black holes. I will discuss soft black hole hair in electrodynamics and in gravitation. Then some speculations on its relevance to the in formation paradox are presented.