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 (firstname.lastname@example.org) 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 (email@example.com).
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.
No Seminar. Friday June 1st.
Roger Bielawski (Leeds). Pluricomplex geometry and quaternionic manifolds. Friday June 8th. Huxley 139, 1.30-2.30pm.
I will describe a new type of geometric structure on complex manifolds. It can be viewed as a deformation of hypercomplex structure, but it also leads to a special type of hypercomplex and hyperkähler geometry. These structures have both algebro-geometric and differential-geometric descriptions, and there are interesting examples arising from physics. Moreover, a class of pluricomplex manifolds leads to quaternion-Kähler metrics, generalising the SO(3)-invariant self-dual Einstein examples of Hitchin.
Marion Moore Campisi (University of Texas, Austin). Bridge distance and exceptional surgeries. Friday June 15th. Huxley 340, 1.30-2.30pm.
In this talk I will discuss ongoing work which shows that links that have high distance bridge surfaces do not admit exceptional surgeries. The distance d(T) of a bridge surface T is defined in terms of the arc and curve complex for the bridge surface and has become a standard way of measuring the “complexity” of the link. This is joint work with Ryan Blair, Jesse Johnson, Scott Taylor and Maggy Tomova.
Andrea Brini (Imperial). A crepant resolution conjecture for open strings. Friday June 22nd. Huxley 139, 1.30-2.30pm.
We propose a Crepant Resolution Conjecture in the context of open Gromov-Witten theory. The content of this talk is based on arxiv:1102.0281 and on joint work in progress with R. Cavalieri (CSU), T. Coates (Imperial) and D. Ross (CSU).
Anne-Sophie Kaloghiros (Imperial). Geography of models and the Sarkisov Program. Friday June 29th. Huxley 139, 1.30-2.30pm.
Given a normal projective variety X and an effective divisor D on X, an important question is to determine whether X has a “good model” for D. When does there exist a birational map X–>X_D, where X_D has manageable singularities and where f_*D is “positive” in a suitable sense? This question can be answered for two remarkable classes of varieties and divisors on them: the first is that of varieties where the Minimal Model Program can be run, and the other that of Mori Dream Spaces. I will define a class that generalizes these two examples, and show how to understand birational maps between good models for distinct divisors. I will give an application to the study of birational maps between Mori fibre spaces (the Sarkisov Program): I will describe generators (work of Hacon-McKernan) and relations in the Sarkisov Program. Part of this talk is based on joint work with Kuronya and Lazic.
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.