# Mathematics Colloquia and Seminars

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### Talks by Guofang Wei (Santa Barbara), David Hoffman (Stanford), Misha Kapovich (UC, Davis).

**Geometry/Topology**

Speaker: | Bay Area Differential Geometry Seminar, UCB, UC Davis, SFSU, UCSC, Stanford |

Location: | 380 Stanford |

Start time: | Sat, Apr 23 2011, 10:00AM |

See the Seminar webpage: http://www.msri.org/web/msri/scientific/show/-/event/Wm8998 BAY AREA DIFFERENTIAL GEOMETRY SEMINAR STANFORD UNIVERSITY, APRIL 23, 2011 Misha Kapovich, University of California, Davis RAAGs in Ham Abstract. “RAAGs” are Right Angled Artin Groups and “Ham” is the group of hamiltonian symplectomorphisms of a symplectic manifold. I will explain how to embed any RAAG in any Ham. In particular, any Ham contains fundamental groups of hyperbolic manifolds for arbitrary dimension. The proof is a combination of topology, geometry and analysis: We will start with embeddings of RAAGs in the mapping class groups of hyperbolic surfaces (topology), then will promote these embeddings to faithful hamiltonian actions on the 2-sphere, supported on a disk (hyperbolic geometry and analysis). David Hofffman, Stanford University Limits of Embedded Minimal Disks Abstract. Given a sequence of properly embedded minimal disks in a subset R3, a subsequence will converge—away from the points where the curvature blows up— to a limit lamination by embedded minimal surfaces. What is the nature of the blowup set? What kinds of limit laminations can occur? I will discuss joint work with Brian White, in which we prove that any closed subset of a line can occur as the blowup set and, surprisingly, catenoids can occur as limit leaves. This contrasts strongly with a famous result of Colding-Minicozzi, Meeks, which states in essence that the only thing that can happen globally is what happens when the disks are rescaled helicoids: the singular set is a line corresponding to the axis Z, and the limit lamination is the foliation of R3 \ Z by punctured planes orthogonal to Z. Our methods work in more general three-manifolds. In particular, they apply to hyperbolic space, where the global results are very different from the Euclidean case. Guofang Wei, University of California, Santa Barbara Comparison Geometry and Ricci Solitons Abstract. Ricci solitons are natural extension of Einstein metrics. They also play an important role in the theory of Ricci flow. We will talk about comparison theorems for smooth metric measure space developed with Will Wylie. We will then apply the volume comparison to study the growth of potential function of gradient steady Ricci soliton. This part of work is joint with Peng Wu.

There will be a banquet dinner. A web-based signup list is provided in the attachment.