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Anthony G. O'Farrell: The Fellowship of the Algebra

(and of the Ring, the Group, and various other algebraic structures in analysis and geometry, etc.) I enjoy working with other people on Mathematical problems, and welcome approaches from all quarters (our students, students elsewhere, faculty in our and other departments, school-teachers, the public at large, anyone with a problem or an interest in discussing a problem).
For my current research concerns, see my summary research page.
For potential research students, my updated list of project proposals is here (in pdf). In general, it's a good idea to start working on your plans for the coming academic year before Christmas.
For schoolteachers who would like to get involved in some research, there is SFI's STARs programme. This funds you to work with people like me during the school holidays. I usually propose some project for consideration. Application are due early each year. Keep an eye on SFI's site.

For teachers and secondary students who like problem-solving, I recommend getting involved in problem-contest activites, such as the Mathematical Olympiads and the High School Maths Contest. I participate in the work of the North Kildare Maths Problem Club, which runs Saturday morning sessions in preparation for the Irish Mathematical Olympiad. If you are new to this kind of thing, I recommend starting with a good book.

Present and former collaborators:

(See my publications page for specific references to joint papers, where applicable.)
Name Topic
John Garnett, Don Marshall, Yaki Sternfeld Approximation problems about sums of algebras of functions (real- and complex-valued).
Ken Preskenis, David Walsh, Alejandro Sanabria, Peter De Paepe, Pascal Thomas, Julien Duval Uniform and Lipschitz norm approximation by polynomials in two complex-valued functions. Polynomial convexity.
Graham Allan, Tom Ransford Tauberian theorems related to power-bounded operators and semigroups
Donal O'Regan Existence results for ODE
Michael Conway, Richard Watson, Declan O'Keeffe Tangent stars and sheaves, and Whitney's extension problem
Fernando Perez-Gonzalez Pointwise-bounded approximation by holomorphic functions
Denise Lord, Hugh Staunton, Edward Keelan Genetics of multiple sclerosis
Graham Allan, Grayson Kakiko, Richard Watson Nachbin's problem about real algebras of smooth functions
Alejandro Sanabria, Ivan Netuka, Pamela Gorkin Pervasive function spaces
Jim Kirk Root-finding and banking problems
Aongus O'Cairbre Convergence of Fourier series.
Michael Brennan, Sean Ashe Mathematics Education
Denise Lord, Tom Dowling, Joan Verdera, Joan Carmona Analytic capacities. Approximation and removability problems for classes of analytic functions.
Fiacre O'Cairbre, Aiden O'Reilly, Jesus San Martin Real dynamical systems and chaos
Sean Dineen, Richard Timoney, Joel Feinsten Fixed points in the maximal ideal space of H infinity.
Joel Feinstein, Harry Lande, Garth Dales Approximation in spaces of infinitely-differentiable functions.
Dymphna Graham, Sinead Keane, Ian Short, Maria Roginskaya, Roman Lavicka, Simon Joyce, Mary Hanley, Denis O'Brien, David Walsh, Richard Watson, Linus Carlsson, Patrick Ahern, Jesus San Martin, Mary Boyce, Yoann O'Donoghue, Ying Hou, Frederic Le Roux, Dmitri Zaitsev, Xianghong Gong, Nick Gill Time-reversal symmetries, reversible maps, groups of maps, flows
Christoph List, Dmitri Zaitsev, Patrick Ahern, Xianghong Gong Complex Dynamics
Gary McGuire, David Redmond, David Wraith, Richard Watson Mathematical Olympiad training
Stephen Buckley, Maria Roginskaya Combinatorics and Graphs
Gavin Armstrong Hausdorff dimension of level sets of smooth functions.
Azadeh Nikou Vector-value function algebras
Patrick Barry School Geometry
Vasily Bernik Problems for children
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Updated 24-3-2022