Landscapes in Mathematical Sciences

This is our Department Colloquium, with distinguished speakers giving an overview of a topic of general mathematical interest. The talks are aimed at a level to be accessible to all postgraduate students and staff in the department. Advanced undergraduates and members of other departments are also welcome to attend.

Talks last a full hour and, unless otherwise stated, take place in the Wolfson Theatre (4W1.7), beginning at 3:15pm. Tea is available from 30 minutes before the talk in the foyer outside the lecture theatre.

Contact


Next Landscapes Seminar

Date Speaker Title/Abstract
17 November 2017 Peter Benner
MPI Magdeburg
Low-rank Techniques: from Matrix Equations to Molecular Physics
The use of low-rank approximations to matrices and tensors has become one of the most successful techniques in Computational Mathematics, Sciences, and Engineering during the last decade. In some, if not many, areas, it has replaced sparsity as the main paradigm to follow for solving extremal large-scale problems. We discuss some of the underlying principles, why and when one can expect low-rank approaches to work. We illustrate the idea of low-rank numerics by examples from the work of the author, ranging from matrix equations to PDE-constrained optimization to molecular physics.

Autumn 2017

Date Speaker Title/Abstract
6 October 2017 Alain Goriely
Oxford
The mathematics and mechanics of brain morphogenesis video link
The human brain is an organ of extreme complexity, the object of ultimate intellectual egocentrism, and a source of endless scientific challenges. Its intricate folded shape has fascinated generations of scientists and has, so far, defied a complete description. How does it emerge? How is its shape related to its function?

In this talk, I will review our current understanding of brain morphogenesis and its unique place within a general mathematical theory of biological growth. In particular, I will present simple models for basic pattern formation and show how they help us understand axonal growth, brain folding, and skull formation.
13 October 2017 Radek Erban
Oxford
Molecular Dynamics, Random Walks and PDEs
I will introduce several deterministic and stochastic dynamical systems which have been used for mathematical modelling in biology, describing processes at different spatial and temporal scales. Using simple illustrative examples, I will discuss connections between (detailed) molecular dynamics simulations, (less detailed) Brownian dynamics approaches and (even coarser) models written as partial differential equations. I will use this discussion to highlight some open mathematical problems in the field of mathematical biology.
27 October 2017 John Parker
Durham
Surfaces from some viewpoints in algebra, geometry and number theory video link
A classical circle of ideas describes a torus as the quotient of the complex plane by a lattice; as the domain of an elliptic function or through the cubic polynomial satisfied by this elliptic function. In turn, the moduli space of such tori is the quotient of the hyperbolic plane by a lattice which is defined arithmetically -- namely the modular group. In this seminar I want to explore several ways these ideas can be extended, thereby linking ideas from geometry (both hyperbolic and algebraic), group theory and number theory.
3 November 2017 Christoph Ortner
Warwick
Atomistic Simulation of Crystalline Defects - [A Case Study from the Perspective of Numerical Analysis] video link

Atomistic simulation is an indispensible tool of modern materials science as it allows scientists to study individual atoms and molecules in a way that is impossible in the laboratory. A key problem of atomistic materials modelling is to determine properties of crystalline defects, such as geometries, formation energies, or mobility, from which meso-scopic material properties or coarse-grained models (e.g., Kinetic Monte-Carlo, Discrete Dislocation Dynamics, Griffith-type fracture laws) can be derived.

In this lecture I will focus on the most basic task: computing the equilibrium configuration of a crystalline defect (time permitting I will comment on other properties). Typical numerical schemes can be interpreted as Galerkin approximations of an infinite-dimensional nonlinear variational problem. This point of view can be effectively employed to study properties of exact solutions and derive rigorous error bounds. It also serves as an excellent test-bed for classifying and benchmarking multi-scale methods such as atomistic/continuum and QM/MM schemes. A key observation is that all these different numerical schemes (classical or multi-scale) simply provide different boundary conditions for the defect core. After this realisation I will conclude the talk by deriving a new boundary condition (work in progress) that promises significantly improved accuracy at negligible increase in computational cost or complexity of algorithms.
17 November 2017 Peter Benner
MPI Magdeburg
Low-rank Techniques: from Matrix Equations to Molecular Physics
The use of low-rank approximations to matrices and tensors has become one of the most successful techniques in Computational Mathematics, Sciences, and Engineering during the last decade. In some, if not many, areas, it has replaced sparsity as the main paradigm to follow for solving extremal large-scale problems. We discuss some of the underlying principles, why and when one can expect low-rank approaches to work. We illustrate the idea of low-rank numerics by examples from the work of the author, ranging from matrix equations to PDE-constrained optimization to molecular physics.
24 November 2017 Reidun Twarock
York
Viruses and Geometry: New Insights into Virus Structure, Assembly, Evolution & Therapy
Viruses are remarkable examples of order at the nanoscale. The capsids of many viruses, enclosing and protecting their genomes, are organised in lattice-like arrangements with overall icosahedral symmetry. Mathematical techniques from group, graph and tiling theory can therefore be used to characterise their architectures. In this talk, I will introduce our mathematical approach to the modelling of viral capsids and its applications in vaccine design. I will then present our Hamiltonian path approach to the modelling of genome packing and virus assembly that underpins the discovery of an assembly instruction manual in a wide range of viruses, including Picornaviruses, Hepatitis C and Hepatitis B virus. Based on these results, I will then construct fitness landscapes in order to model viral evolution and compare different forms of anti-viral therapy.

A list of talks in recent past years can be found here.