Summer term 2012
Various speakers. Geometry Day III. Friday May 4th. King’s College London.
Geometry Day III will be taking place on 4 May 2012 in K0.16, King’s Building, Strand Campus of King’s College London.
Speakers are: Simon Donaldson, Francisco Lopez, Baris Coskunuzer, Carlo Sinestrari and YanYan Li.
If you would like to attend, please contact Emily Balls (emily.balls@kcl.ac.uk) with your name, email address and institution, ideally by 20 April 2012. Please also indicate whether you are interested in attending the dinner for which there will be a nominal fee. Any academic questions should be directed to Dr Giuseppe Tinaglia (giuseppe.tinaglia@kcl.ac.uk).
More information at www.kcl.ac.uk/nms/depts/mathematics/geometry3.aspx
Marc Lackenby (Oxford). Links with splitting number one. Friday May 11th. Huxley 139, 1.30-2.30pm.
The unknotting number of a knot is an incredibly difficult invariant to compute. In fact, there are many knots which are conjectured to have unknotting number 2 but for which no proof of this is currently available. It therefore remains an unsolved problem to find an algorithm that determines whether a knot has unknotting number one. In my talk, I will show that an analogous problem for links is soluble. We say that a link has splitting number one if some crossing change turns it into a split link. I will give an algorithm that determines whether a link has splitting number one. (In the case where the link has two components, we must make a hypothesis on their linking number.) The proof that the algorithm works uses sutured manifolds and normal surfaces.
Gabor Szekelyhidi (University of Notre Dame). Filtrations and test-configurations. Friday May 18th. Huxley 139, 1.30-2.30pm.
Test-configurations are certain degenerations of projective manifolds, which are used in the definition of K-stability. I will explain how filtrations of the homogeneous coordinate ring of a projective manifold can be thought of as sequences of test-configurations, and that they encode the limiting behavior of these sequences. These filtrations arise naturally when studying the Calabi flow, or when trying to minimize the Calabi functional. I will also discuss how filtrations can be used to give a strengthening of the notion of K-stability, and why this is desirable.
Jan Christophersen (University of Oslo). Simplicial complexes and projective varieties. Friday May 25th. Huxley 139, 1.30-2.30pm.
The Stanley-Reisner construction associates to a simplicial complex a projective scheme which “looks like” the complex. For combinatorial manifolds, if the scheme is smoothable, it will smooth to special algebraic varieties. For example a sphere will in this way correspond to a Calabi-Yau manifold and a torus to an abelian variety. It turns out that interesting triangulations of manifolds yield interesting algebraic geometry via deformations of Stanley-Reisner schemes and I will describe this connection with several examples.
TBD. Friday June 1st. Huxley 139, 1.30-2.30pm.
Roger Bielawski (Leeds). TBA Friday June 8th. Huxley 139, 1.30-2.30pm.
Marion Moore Campisi (University of Texas, Austin). TBA . Friday June 15th. Huxley 340, 1.30-2.30pm.
Andrea Brini (Imperial). TBA Friday June 22nd. Huxley 139, 1.30-2.30pm.
Anne-Sophie Kaloghiros (Imperial). TBA Friday June 29th. Huxley 139, 1.30-2.30pm.
Vincent Borrelli (Lyon) and Etienne Ghys (CNRS, Lyon). LMS Hardy Lecture. Friday June 29th. University College London, 3.30-6.30pm.
Vincent Borrelli will speak on Flat tori in three-dimensional space at 3.30, and Etienne Ghys will speak on Cutting cloth according to Chebyshev at 5.15. Both talks will be directed at a general mathematical audience. A reception will follow at 6.30 at a cost of £35 per person. See http://www.lms.ac.uk/sites/default/files/files/posters/Hardy%2012%20poster.pdf for more details and for contact information.