CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR : | Hossein MovasatiIMPA |
A conjectural Hodge locus for cubic tenfold |

on Wednesday, December 12, 2018, at 1:30 - 3:00 pm in CMSA Building, 20 Garden St, G10 | ||

In this talk we will consider the difference of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold, for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces. |

CMSA COLLOQUIUM: | Zhiwei YunMIT |
Shtukas: what and why |

on Wednesday, December 12, 2018, at 4:30 pm in CMSA Building, 20 Garden St, G10 | ||

This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them. |

STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR: | Fenglong YouUniversity of Alberta |
Mirror theorems for orbifold and relative Gromov-Witten invariants |

on Friday, December 14, 2018, at 2:00 - 3:15 pm in Science Center 507 | ||

Enumerative mirror symmetry can be stated as the relation between generating functions(J-functions) of Gromov--Witten invariants and period integrals(or the I-functions). Such relations are called mirror theorems. We obtained a mirror theorem for orbifold Gromov-Witten invariants of root stacks. Using the relation between relative and orbifold Gromov-Witten invariants, we also obtain a mirror theorem for relative Gromov-Witten invariants. This is joint work with Honglu Fan and Hsian-Hua Tseng. |