Part of the series 'What do historians of mathematics do?'

I'm currently working on a biography of Charles Hutton (1737–1823): pit lad, FRS, and professor of Mathematics. No-one much has heard of him today, but to his contemporaries he was "one of the greatest mathematicians in Europe". I'll give an outline of his remarkable story and say something about why he's worth my time.

Part of the series 'What do historians of mathematics do?' 

" Over the last four centuries a huge amount of mathematics has been published.  Most of it has, however, had little or no influence.  By way of contrast, some mathematics, although unpublished in its time, has had great influence.  My hope is to illustrate this with discussion of manuscript sources and resources that have survived from Thomas Harriot (c.1560--1621), Isaac Newton (1642--1727) and Évariste Galois (1811--1832)."

Sasakian manifolds are odd-dimensional counterparts of Kahler manifolds in even dimensions, 
with K-contact manifolds corresponding to symplectic manifolds. It is an interesting problem to find
obstructions for a closed manifold to admit such types of structures and in particular, to construct
K-contact manifolds which do not admit Sasakian structures. In the simply-connected case, the
hardest dimension is 5, where Kollar has found subtle obstructions to the existence of Sasakian 
structures, associated to the theory of algebraic surfaces.
In this talk, we develop methods to distinguish K-contact manifolds from Sasakian ones in 
dimension 5. In particular, we find the first example of a closed 5-manifold with first Betti number 0 which is K-contact but which carries no semi-regular Sasakian structure.

 (Joint work with J.A. Rojo and A. Tralle).

Black holes are one of the few available laboratories for testing theoretical ideas in fundamental physics. Since Hawking's result that they radiate a thermal spectrum, black holes have been regarded as thermodynamic objects with associated temperature, entropy, etc. While this is an extremely beautiful picture it has also lead to numerous puzzles. In this talk I will describe the two-loop correction to scalar correlation functions due to \phi^{^4} interactions and explain why this might have implications for our current view of semi-classical black holes.
 

For linear dynamical systems, model reduction has achieved great success. In the case of linear dynamics,  we know how to construct, at a modest cost, (locally) optimal, input-independent reduced models; that is, reduced models that are uniformly good over all inputs having bounded energy. In addition, in some cases we can achieve this goal using only input/output data without a priori knowledge of internal  dynamics.  Even though model reduction has been successfully and effectively applied to nonlinear dynamical systems as well, in this setting,  bot the reduction process and the reduced models are input dependent and the high fidelity of the resulting approximation is generically restricted to the training input/data. In this talk, we will offer remedies to this situation.