MATHEMATICAL PHYSICS SEMINAR : | Daniel HarlowHARVARD UNIVERSITY |
Operator Algebras and Entropy in Lattice Gauge Theory |

on Tuesday, November 24, 2015, at 1:15 pm in Jefferson 453 |

MATHEMATICAL PHYSICS SEMINAR : | Victor KacMASSACHUSETTS INSTITUTE OF TECHNOLOGY |
Algebraic Theory of Integrable Systems |

on Tuesday, November 24, 2015, at 4:15 PM in Jefferson 356 |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR: | Hongwei XuCMS at Zhejiang University |
Mean curvature flow meets Ricci flow: Convergence and sphere theorems of submanifolds arising from Yau rigidity theory |

on Tuesday, November 24, 2015, at 10:00 AM in Science Center 232 | ||

In 1975, S.-T. Yau established the rigidity theory of CMC submanifolds, which plays an important role in the study of the mean curvature flow, and curvature and topology of submanifolds. During the past four decades, the Yau rigidity theory has been developed by several geometers and I. Using the Ricci flow and stable currents, Xu-Zhao initiated the study of differential pinching problem of submanifolds. Afterwards, Gu-Xu extented Brendle-Schoen's 1/4-pinching differentiable sphere theorm to the case of submanifolds in a Riemannian manifold with arbitrary codimension $p(\ge 0)$. As a consequence, we proved an optimal differentiable sphere theorm for submanifolds in Euclidean spaces. It’s the first optimal differentiable sphere theorem for submanifolds of arbitrary dimension and codimension. Mean while, by using the mean curvature flow, Andrews-Baker obtained the same differentiable sphere theorm for submanifolds in Euclidean spaces independently. Later Baker and Liu-Xu-Ye-Zhao proved a sharp convergence theorem for the mean curvature flow of submanifolds in space forms. Recntly, my students and I proved several new sphere theorems for submanifolds via the Ricci flow. Most recently, motivated by the Yau rigidity theory and by developing new techniques, Lei and I verified a new sharp convergence theorem for the mean curvature flow of submanifolds in spheres and an optimal convergence theorem for the mean curvature flow of submanifolds in hyperbolic spaces, which improve the convergence theorems due to Baker, Huisken and Liu-Xu-Ye-Zhao. Notice that Andrews-Baker-Gu-Xu’s optimal pinching condition implies positivity of the sectional curvature. Lei-Xu’s pinching condition implies that the Ricci curvature of the initial submanifold is positive, but does not imply positivity of the sectional curvature. Consequently, we obtain an optimal differentiable sphere theorem for submanifolds in hyperbolic spaces and a new differentiable sphere theorem for submanifolds in spheres. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR: | Roger CasalsMIT |
Legendrian Presentation of Weinstein Domains |

on Monday, November 30, 2015, at 12:00 - 2:00 PM in Science Center 232 | ||

In this talk we will discuss the Legendrian front description of Weinstein manifolds. This provides diagramatic computations of wrapped Fukaya categories and the symplectic coho- mology for certain Weinstein domains, which feature on the A{side of Homological Mirror Symmetry. The required denitions and necessary results will be provided. In the rst part, we present the dictionary between Legendrian presentations and adapted open books decompositions. In the second part, we explore applications to Weinstein cobordisms, ex- act Lagrangians and biLefschetz brations with Am{Milnor bres. This is joint work with E. Murphy. |

DIFFERENTIAL GEOMETRY SEMINAR: | Bong LianBRANDEIS UNIVERSITY |
Large complex structure limits of Calabi-Yau manifolds |

on Tuesday, December 01, 2015, at 4:15 PM in Science Center 507 | ||

LCSL's are special types of degenerations CY manifolds that play an important role in mirror symmetry. They are known to exist for a large class of cases which I will briefly review. We then discuss some new constructions of these LCSLs. This is based on joint work with S. Bloch, A. Huang, D. Srinivas, S.-T. Yau, and X. Zhu. |

MATHEMATICAL PHYSICS SEMINAR : | Sörin PetratIST, Austria |
Derivation of Mean-field Dynamics for Fermions |

on Tuesday, December 08, 2015, at 1:15 pm in Jefferson 453 |

MATHEMATICAL PHYSICS SEMINAR : | Roland BauerschmidtHARVARD UNIVERSITY |
Renormalization Group Analysis of Self-Avoiding Walk and Spin Models in 4D |

on Tuesday, December 08, 2015, at 4:15 PM in Jefferson 356 |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Matthew J. HolmanHARVARD SMITHSONIAN CENTER FOR ASTROPHYSICS |
Dynamical Chaos in Kepler Planetary Systems |

on Wednesday, December 09, 2015, at 4:00 - 5:00 PM in Science Center 507 | ||

Of the Kepler planets that have been reported to date, a significant fraction are in systems with multiple transiting planets. In some cases, the signature of the gravitational interactions between planets in these systems can be seen in the variations of their times of transit. By carefully modeling the transit times, as well as investigating long-term stability, we are able to measure or constrain the masses and orbits of the transiting bodies in some of these systems, verifying that they are indeed planets. Although this approach is particularly effective for closely packed and near-resonant systems, it has also been applied to a broad range of systems. These include circumbinary planets, as well as systems with additional non-transiting planets. Some of the Kepler planetary systems exhibit evidence of dynamical chaos on remarkably short time scales, yet these systems are likely to be long-lived. I will highlight the theoretical advances in our understanding of dynamical chaos and stability that have been prompted by the Kepler planetary systems. |