Final year projects, TCD 2007-...
MA4491/4492 is an optional module for students in their final year that offers some research experience in the shape of a half-year or a full-year project. Feel free to contact me (or any other staff member of School of Maths, to that matter) about topics for final year projects; I think that solving some problem as a project is more fun, but I can suggest reading–oriented projects as well. Your name can easily end up on the list below!
Year 2018/19
Oisín Flynn-Connolly, "Pre-Lie universal enveloping algebras"David Glynn, "Automatic geometric theorem proving"
Peter Phelan, "Laplacians for truncated Lie algebras: computations and conjectures"
Year 2017/18
Daniel Mulcahy and Peter Phelan, "Counting dimensions of tangent spaces to Hilbert schemes of points" (summer internship)Kealan Daly, "Hypergeometric series, creative telescoping, and a Ramanujan-type supercongruence"
Ogden Deacon, "Saddle-point methods in analytic combinatorics"
Darren Rice, "Combinatorial species and the Lagrange inversion formula"
Year 2016/17
I was on a research leave and did not supervise any projectsYear 2015/16
Adam Keilthy, "Toric varieties of brick polytopes, associahedra and operad structures"Callum MacIver, "Dimensionality of Lie elements in the symmetric group algebra"
Louis Mahon, "Invariant theory"
Conor McMeel, "Extensions of simple modules of the symmetric group over a field of positive characteristic"
Year 2014/15
Ewan Dalby, "Catalan numbers, nonsymmetric operads, and Gröbner bases"Year 2013/14
Daron Anderson, "Topological groups"Jackson Aurisch, "Hasse–Minkowski principle"
Benen Harrington, "Topological data analysis"
Year 2012/13
Shane Sheedy, "Patterns in labelled trees" (summer internship)Stiofáin Fordham, "Topics in invariant theory"
Jack Kelly, "Boson–Fermion Correspondence"
Year 2010/11
Eoin Murphy, "Posets and algebraic topology" (summer internship)Ronan Darcy, "Topological proof(s) of Abel's theorem"
Ruadhai Dervan, "Hilbert schemes of points"
Josh Tobin, "A case study of Gröbner bases and Anick's resolution"
Year 2009/10
Nick Byrne, "Basics of representation theory and finite dimensional representations of the relation x2+y2=xy" (summer internship)Sean Damery, "Complex numbers, quaternions, and sums of squares" (summer internship)