St Patrick's College hosts Mathematics Research Seminar

The Department of mathematics was proud to host Dr. Brendan Guilfoyle as research visitor at St.Patrick's College.  Dr. Guilfoyle, from IT Tralee, is a renowned mathematician, particularly for his recent solution to an almost century old, unsolved, maths puzzle.

The famous 'Caratheodory Conjecture' dates back to 1923 and since then though it has been attempted by many mathematicians, its solution remained elusive.  Only very recently Dr. Guilfoyle, in collaboration with Dr. Klingenberg, presented a solution to the problem using modern geometry.  It turns out that one has to move away from the classical methods of differential equations and use very novel ideas about the geometry of lines in Euclidean space.   Dr. Guilfoyle gave a seminar presentation, called, "Line geometry and Euclidean geometry", on July 13th, about this work.  He introduced new geometric structures on the space of lines, including the notions of negative length and zero area.  These new structures also have applications to geometric optics, which he illustrated with many beautiful pictures of optical wave fronts.  He then proceeded to give a brief sketch of the solution to the Caratheodory Conjecture, using modern techniques of line geometry, symplectic geometry and the theory of mean curvature flows.

The seminar was well attended by faculty from DCU, UCD, Trinity College, St.Patrick's College and the general public.  It was followed by an informal discussion session in the college staff room.

Dr. Brendan Guilfoyle is a reasearch collaborator of Dr. Madeeha Khalid at St. Patrick's College.  Currently they are investigating the possible existence of a group law (analogous to addition of numbers) on the space of oriented lines.

 

 

 

Last Updated: Monday July 20 2009