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Anthony O'Farrell's Personal Pages
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Analysis. Singularities, Extensions, and Approximations. Dynamical Systems, Algebraic structures in Analysis and Geometry.
Mathematics is densely interconnected. Temperamentally, the centre of my interest is in analysis. I particularly like the amazing things that happen in Complex Analysis, which still seems magic to me, after all these years. I also like qualitative approximation problems. Most of the things I've studied grow out of these two areas, in some way. The interplay between algebraic structure and concepts from analysis is a theme that has proven enormously fruitful, and has a lot of energy left. The structures I have found most useful are algebras over the field of complex numbers. In the past few years, I've been exploring groups of maps. Geometric insight can also be brought to bear on problems in analysis (and algebra). I've seen that probability can provide the key to solving problems that don't seem to have
any uncertainty about them. Intuition derived from the physics of Hamiltonian dynamical systems or of the Brownian motion have been valuable to me, even in situations which are very un-physical.
The record of completed research work may be viewed by following the link to my publications.
Some current concerns are listed in my projects file.
At most times I am happy to talk to anyone about mathematics at the drop of a hat. Proposals for regular periodic bilateral conversations are normally accepted. I have discovered that it is usually better to say yes.