## Mathematics Colloquium 2012 - 2013

### Programme

All seminars are held in Room E/0.15, Senghennydd Road, Cardiff at 15:10 unless stated otherwise.

Further information is available from Dr Federica Dragoni at DragoniF@cf.ac.uk

##### 31st October 2012

**Speaker: **Jack Gondzio (University of Edinburgh)

**Title:** Interior Point Methods for Large Scale Optimization.

**Room**: E/0.15

**Abstract: **Interior Point Methods (IPMs) for linear, quadratic and nonlinear optimization have been around for more than 25 years and have completely changed the field of optimization. In the first part of my talk I will focus on the major features responsible for their spectacular success:

(a) nice properties (self-concordance) of logarithmic barriers which are responsible for the polynomial complexity of IPMs,

(b) a unified view of IPMs for linear, quadratic, convex nonlinear, second-order cone, and semidefinite optimization,

(c) IPMs' ability to solve very large problems.

In the second part of my talk I will address the theoretical issues of applying the *inexact* Newton method in an IPM and a redesign of the method bearing two objectives in mind:

(a) to avoid an explicit access to the problem data and to allow only matrix-vector products to be executed with the Hessian and Jacobian and its transpose; and

(b) to allow the method work in a limited-memory regime.

If time permits, I will present the numerical results which demonstrate the practical performance of the new approach applied to four classes of challenging optimization problems:

- relaxations of quadratic assignment problems,

- quantum information problems,

- sparse approximation problems arising in compressed sensing,

- PageRank (google) problems.

##### 14th November 2012

**Speaker: **Chris Budd (University of Bath)

**Title:** Monge Ampere based adaptive methods with applications to meteorology.

**Abstract: **TBA.

##### 27th February 2013

**Speaker: **Professor Keith Ball (University of Warwick)

**Title:** Entropy Growth in the Central Limit Theorem.

**Abstract: **The talk explains how a geometric principle gave rise to a new

variational description of information-theoretic entropy and how this

led to the solution of a problem dating back to the 50's: whether the

the central limit theorem is driven by an analogue of the second law

of thermodynamics..

##### 17th April 2013

**Speaker: **Terry Lyons (University of Oxford)

**Title:** What can rough paths do for you.

**Abstract: **This is a general talk for a scientific audience - aimed at exploring the power of abstract mathematical ideas - and then finishing with an introduction to a new set of ideas, developed over the last 20 years, known as rough path theory. This theory has at its heart new mathematical tools for describing the macroscopic interaction between complex (oscillatory) systems. The tools are mathematically precise and rather abstract, but they are also numerically informative and offer effective ways to describe and think about oscillatory data. We will mention some applications in finance and in sound compression. Further development of this theory are, through the amazing work of Hairer, impacting on the fundamentals of PDE theory and other contributions are now connecting to John Cardy's work on constructive conformal field theory and SLE, but the talk will not try to discuss these developments.