## Past Seminars by Series

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. |

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

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

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

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

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

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

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 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. |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. |

Thu Apr 25 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Harmonic surfaces and simple loops Vlad Markovic - Ordway Visitor, Caltech |

Tue Apr 23 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Self-homeomorphisms of reducible 3-manifolds and applications in topology, geometry and dynamics. Christoforos Neofytidis, University of Geneva We recall the self-homeomorphisms of a closed oriented reducible 3-manifold. Using this description, we discuss various problems in low-dimensional topology and dynamics, such as the existence of Anosov tori in 3-manifolds (joint work with Shicheng Wang), the simplicial volume of mapping tori of 3-manifolds (joint work Michelle Bucher) and the virtual Betti numbers of mapping tori of 3-manifolds. |

Thu Dec 20 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Projective Geometry, Complex Hyperbolic Space, and Geometric Transitions Steve Trettel, UC Santa Barbara The natural analog of Teichmuller theory for hyperbolic manifolds in dimension 3 or greater is trivialized by Mostow Rigidity, so mathematicians have worked to understand more general deformations. Two well studied examples, convex real projective structures and complex hyperbolic structures, have been investigated extensively and provide independently developed deformation theories. Here we will discuss a surprising connection between the these, and construct a one parameter family of geometries deforming complex hyperbolic space into a new geometry built out of real projective space and its dual. This connects the aforementioned deformation theories and provides geometric motivation for a representation-theoretic observation of Cooper, Long, and Thistlethwaite |

Thu Dec 06 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Enumerative geometry: old and new Felix Janda, University of Michigan For as long as people have studied geometry, they have counted In this talk, I will show how to solve several classical counting |

Fri Oct 19 |
## Differential Geometry and Symplectic Topology Seminar2:30pm - Vincent Hall 6The Smooth 4-dimensional Poincare Conjecture and Dehn surgery on links Alex Zupan, University of Nebraska The smooth version of the 4-dimensional Poincare Conjecture (S4PC) states that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere. One way to attack the S4PC is to examine a restricted class of 4-manifolds. For example, Gabai's proof of Property R implies that every homotopy 4-sphere built with one 2-handle and one 3-handle is standard. In this talk, we consider homotopy 4-spheres X built with two 2-handles and two 3-handles, which are uniquely determined by the attaching link L for the 2-handles in the 3-sphere. We prove that if one of the components of L is the connected sum of a torus knot T(p,2) and its mirror (a generalized square knot), then X is diffeomorphic to the standard 4-sphere. This is joint work with Jeffrey Meier. |

Thu Oct 04 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Stability of Ricci solitons Huaidong Cao - Ordway Visitor, Lehigh University In this talk we continue our discussion of the previous week on stability of |

Thu Sep 27 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Second variation of Perelman's entropy and stability of Ricci solitons Huaidong Cao, Ordway Visitor, Lehigh University Einstein metrics are critical points of the well-known classical Hilbert action |

Thu Sep 20 |
## Differential Geometry and Symplectic Topology Seminar1:25pm - Vincent Hall 570Monotonicity formulas and Type I singularities Huaidong Cao, Ordway Visitor, Lehigh University In this talk we shall introduce Huisken's monotonicity formula for the mean curvature flow and Perelman's monotonicity formulas for the Ricci flow. We shall discuss their applications, including the role they play in studying Type-I singularities of the flows. |