GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR: | R. Inanc BaykurUNIVERSITY OF MASSACHUSETTS AMHERST |
Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds |

on Friday, January 30, 2015, at 3:30 PM in Science Center 507 | ||

We initiate an extensive study of multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups. Using our techniques, we can reformulate and tackle various interesting conjectures and problems related to the topology of symplectic 4-manifolds. In this talk we will focus on the conjectural smooth classification of symplectic Calabi-Yaus and their fundamental groups in real dimension 4. If time permits, we will discuss some other applications as well; such as Stipsicz's conjectures on minimality and fiber sum decompositions, constructions of inequivalent Lefschetz fibrations and exotic pencils. Several parts of this work is joint with K. Hayano and N. Monden. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR: | Peng ZhaoSIMONS CENTER FOR GEOMETRY & PHYSICS, STONY BROOK |
Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories |

on Monday, February 02, 2015, at 12:00 - 2:00 PM in Science Center 232 |

DIFFERENTIAL GEOMETRY SEMINAR: | Valentino TosattiNORTHWESTERN UNIVERSITY |
Degenerations and collapsing of Ricci-flat Calabi-Yau manifolds |

on Tuesday, February 03, 2015, at 4:15 PM in Science Center 507 | ||

I will discuss the problem of understanding how Ricci-flat Calabi-Yau manifolds degenerate and collapse to lower-dimensional spaces, and how this is relevant to the Strominger-Yau-Zaslow picture of mirror symmetry. I will present some results in this direction, which are joint work with M.Gross, Y. Zhang, with H.J. Hein and with B. Weinkove, X. Yang. |

INFORMAL DYNAMICS & GEOMETRY SEMINAR: | Ronen MukamelUNIVERSITY OF CHICAGO |
Kronecker's congruence and Teichmüller curves in positive characteristic |

on Wednesday, February 04, 2015, at 4:00 PM in Science Center 507 |

HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR: | Klaus HulekLeibniz University Hannover |
Stable cohomology of compactifications of Ag |

on Tuesday, March 10, 2015, at 3:00 PM in Science Center 507 | ||

A well known result of Borel says that the cohomology of Ag stabilizes. This was generalized to the Satake compactification by Charney and Lee. In this talk we will discuss whether the result can also be extended to toroidal compactifictaions. As we shall see this cannot be expected for the second Vornoi compactification, but we shall show that the cohomology of the perfect cone compactification does stabilize. We shall also discuss partial compactifications, in particular the matroidal locus. This is joint work with Sam Grushevsky and Orsola Tommasi. |