## Seminar Categories

## Current Series

Thu Sep 19 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570D=4, N=1 Compactifications of Maximal Supergravities via Generalised Geometry - Kahler potentials, superpotentials and moduli David Tennnyson, Imperial College London We analyse compactifications of 11 dimensional or type II supergravity down to 4 dimensional Minkowski space for generic flux and generic internal Killing spinors. We note the failure of conventional differential geometry to capture the generic features of the theory and show that the correct formalism comes in the form of a closed form Leibniz algebroid - or as we call it in the physics community, generalised geometry. Our structure is similar to the generalised geometry of Hitchin, but now the structure group is the non-compact exceptional group E_{7(7)}x R^{+}. It turns out that having N=1 supersymmetry in the effective theory on Minkowski space is equivalent to an integrable SU(7) structure on the generalised tangent bundle. We provide the tensors that define the SU(7) structure and give the integrability conditions. Finally we provide an expression for the Kahler potential on the space of structures, the superpotential of the lower dimensional theory, and we explore the moduli of these structures giving explicit answers in certain cases. |

Tue Sep 24 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Sep 26 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Oct 01 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Oct 03 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Oct 08 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Oct 10 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Oct 15 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Oct 17 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Oct 22 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Oct 24 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Oct 29 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Oct 31 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Nov 05 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Nov 07 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Nov 12 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Nov 14 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Nov 19 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Nov 21 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Geometry of degenerating Calabi-Yau manifolds Ruobing Zhang, Stony Brook This talk concerns a family of "collapsing" Ricci-flat Kähler manifolds, namely Calabi-Yau manifolds, converging to a lower dimensional limit, which develop singularities arising in various contexts such as metric Riemannian geometry, complex geometry and degenerating nonlinear equations. A primary aspect is to formulate how well behaved or badly behaved such spaces can be in terms of the recently developed regularity theory. Under the above framework, our next focus is on a longstanding fundamental problem which is to understand singularities of collapsing Ricci-flat metrics along an algebraically degenerating family. We will give accurate characterizations of such metrics and explain possible generalizations. |

Mon Nov 25 |
## Differential Geometry and Symplectic Topology Seminar10:10am - Vincent Hall 203ADifferential Signatures and Algebraic Curves Michael Ruddy,, Max Planck Institute For the action of a group on the plane, the group equivalence problem for curves can be stated as: given two curves, decide if they are related by an element of the group. The signature method, using differential invariants, to answer the local group equivalence problem for smooth curves and its application to image science has been extensively studied. For planar algebraic curves under subgroups of the general linear group, we show that this provides a method to associate a unique algebraic curve to each equivalence class, the algebraic curve's signature curve. However, computing the implicit equation of the signature curve is a challenging problem. In this talk we consider signatures of algebraic curves, show how to compute the degree without computing its defining polynomial explicitly, and present some results on the structure of signature curves for generic algebraic curves of fixed degree. Additionally we show that this leads to a method to solve the group equivalence problem for algebraic curves using numerical algebraic geometry. |

Thu Nov 28 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Dec 03 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Dec 05 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Einstein's gravity and stability of black holes Pei-Ken Hung, MIT Though Einstein's fundamental theory of general relativity has already celebrated its one hundredth birthday, there are still many outstanding unsolved problems. The Kerr stability conjecture is one of the most important open problems, which posits that the Kerr metrics are stable solutions of the vacuum Einstein equation. Over the past decade, there have been huge advances towards this conjecture based on the study of wave equations in black hole spacetimes and structures in the Einstein equation. In this talk, I will discuss the recent progress in the stability problems with special focus on the wave gauge. |

Tue Dec 10 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology Seminar TBA |

Thu Dec 12 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Tue Dec 17 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Dec 19 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Differential Geometry and Sympletic Topology TBA |

Thu Mar 05 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570An invitation to contact homology Erkao Bao, Scientist at the company Houzz in Palo Alto Contact homology is an invariant of the contact structure, which is an odd-dimensional counterpart of a symplectic structure. It was proposed by Eliashberg, Givental and Hofer in 2000. The application of contact homology and its variants include distinguishing contact structures, knot invariants, the Weinstein conjecture and generalization, and calculating Gromov-Witten invariants. In this talk, I will start with the notion of contact structures, then give a heuristic definition of the contact homology as an infinite dimensional Morse homology, and finally explain the major difficulties to make the definition rigorous. This is a joint work with Ko Honda. |