# Colloquium Ical Atom Mailing List

## This Week

#### Misha Verbitsky (*IMPA*)

Teichmuller spaces for geometric structures and the mapping class group action

Teichmuller spaces for geometric structures and the mapping class group action

The Teichmuller space of geometric structures of a given type is a quotient of the (generally, infinite-dimensional) space of geometric structures by the group of isotopies, that is, by the connected component of the diffeomorphism group. In several important qand smooth.uestions, such as for symplectic, hyperkahler, Calabi-Yau, G2 structures, this quotient is finite-dimenisional and even smooth. The mapping class group acts on the Teichmuller space by natural diffeomorphisms, and this action is in many important situations ergodic (in particular, it has dense orbits), bringing strong consequences for the geometry. I would describe the Teichmuller space for the best understood cases, such as symplectic and hyperkahler manifolds, and give a few geometric applications.

## 2022–23–B meetings

### Upcoming Meetings

Date |
Title |
Speaker |
Abstract |
---|---|---|---|

Jun 6 | Teichmuller spaces for geometric structures and the mapping class group action | Misha Verbitsky (IMPA) | |

Jun 13 | Ergodic theory and symplectic packing | Misha Verbitsky (IMPA) | |

Jun 20 | Eigenvalues of the hyperbolic Laplacian and Random Matrix Theory | Zeev Rudnick (Tel Aviv University) |

### Past Meetings

Date |
Title |
Speaker |
Abstract |
---|---|---|---|

Apr 18 | Meeting | Department meeting | |

May 2 | Some recent applications of model theory to algebraic vector fields. | Rahim Moosa (University of Waterloo) | |

May 9 | Sets of non-Lyapunov behaviour for matrix cocycles | Sasha Sodin (Queen Mary University of London) | |

May 16 | On the abominable properties of the Almost Mathieu Operator with Liouville frequencies | Mira Shamis (Queen Mary University of London) | |

May 23 | Kahler-type symplectic embeddings of balls into symplectic manifolds | Michael Entov (Technion) |

Seminar run by Dr. Michael Brandenbursky