Trinity College Dublin’s School of Mathematics recently welcomed leading mathematicians from across the globe to its annual William Rowan Hamilton Geometry and Topology Workshop. The workshop consisted of a two-day mini course which was then followed by a three-day lecture series.
Sir William Rowan Hamilton (1805-1865), a former professor at Trinity, was a leading physicist, astronomer and mathematician, who made important contributions to classical mechanics, optics and algebra. He is perhaps best known for inventing the quaternions, a set of complex numbers that are able to map the orientation and rotation of objects in three-dimensional space (such as in computer graphics).
The primary goal of the workshop was to provide a forum in which the international geometry and topology community can meet with its European counterpart, to discuss topics of an interdisciplinary nature. A major anticipated outcome of these annual workshops is the determination of future research directions, and the generation of a list of open problems in the topics of focus.
Dr Vladimir Dotsenko, Assistant Professor in Pure & Applied Mathematics at Trinity, was on the organizing committee. He said:
“For 10 years this has been one of the biggest international events in pure mathematics hosted by an Irish university, and Trinity College is very excited to be the continuing host of this event.”
“In addition to a research workshop which brings together experts in the field delivering talks on frontiers of research in geometry and topology, every year a mini-course is organised so that the younger participants of the workshop get an introduction to recent developments in a more accessible way.”
The workshop was hosted by the Hamilton Mathematics Institute at Trinity, and was also supported by the National Science Foundation, Boston College, and Science Foundation Ireland. Among the distinguished speakers this year was Professor Jeff Brock, from Brown University in the USA. Professor Brock gave a lecture that formed part of the public event of this workshop.
He added: “Each year I’m increasingly impressed by how well involved young mathematicians are in the early mini-courses, and how nicely their enthusiasm bolsters the research lectures by more senior researchers during the main body of the workshop. The last few years have represented a significant sea change in the direction of the fields of geometry and topology - with the solution of many outstanding fundamental conjectures (due to Henri Poincaré, William Thurston and others) the field has taken on a new tenor of which Hamilton would no doubt have approved: more dynamic and probabilistic methods for understanding the ‘shape of space’ have emerged.”
“This year’s conference sought to reconcile new breakthroughs in the algebraic underpinnings of the field with the modern dynamical and geometric perspectives. The conference did a great deal to push past a potentially worrisome ‘two-cultures’ division and get these different sides of the field in much closer contact. The city of Dublin itself, with its lively cultural environment, and Trinity College, with its congenial atmosphere and venerable history, provided an ideal location for this sort of intellectual communion. It’s an honour and a pleasure to have been able to take part in this tradition."