Department of Mathematics
UCL, Gower Street, London, WC1E 6BT
University College London, 4th December 2013. 14:00 - 17:00
Are you a third or fourth year undergraduate?
Are you interested in geometry or topology?
We are hosting an event for undergraduates which will provide an elementary introduction to current research in geometry and topology, as well as discussing the process and demands of studying for a PhD in these areas. This is also a great opportunity to find out more about the new London School of Geometry and Number Theory, an EPSRC-funded Doctoral Training Centre joint between UCL, KCL and Imperial College London. The first cohort will start in October 2014 and applications are already open.
Room D103 (First floor 25 Gordon Street, the UCLU building)
14:00 - 14:15 Welcome by Robb McDonald, Head of Department
14:15 - 15:15 Short talks by Felix Schulze (UCL), Jonny Evans (UCL), Fyodor Gainullin (Imperial), Henry Wilton (UCL) and Konstanze Rietsch (KCL).
15:30 - 16:15 Short presentations on funding by John Talbot and Michael Singer and question/answer session with the group and current PhD students
Room 502 (Fifth floor of 25 Gordon Street, the UCLU building)
16:30 - 17:30 Reception and informal discussions
Image courtesy of: Imaging Technology Group, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Illinois, USA.
The picture shows some fibres of the Hopf fibration, a fibring of the three-sphere by linked circles. The space of fibres is the two-sphere and the corresponding map from the three-sphere to the two-sphere is the simplest map with nonzero Hopf invariant. See this page for a beautiful explanation and accompanying video.
The fibres chosen here all live on the (stereographically projected) Clifford torus. The Lawson conjecture states that this is the only minimally embedded torus in the three-sphere (up to isometry) - this conjecture was recently proved by S. Brendle, after being open for more than forty years.
It also arises as a global minimiser for the Willmore energy functional on embedded surfaces in the three-sphere of genus at least one. This Willmore conjecture had been open since 1965 and was recently proved by Marques and Neves.