# Logic seminar: Boris Zilber (University of Oxford)

Dates: | 8 November 2023 |
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Times: | 15:15 - 16:15 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Title: Model theory and topological invariants of algebraic varieties.

Abstract: Can model theory distinguish complex algebraic varieties which are isomorphic as structures but topologically different? I am going to present evidence that a categorical $L_{\omega_1,\omega$ sentence $\Sigma_X$ describing the universal cover of a complex algebraic variety $X$ is a very strong invariant. Namely, if a complex variety $X'$ is a model of $\Sigma_X$ then $X'$ is biholomorphically isomorphic to $X$ or to a complex conjugate of $X.$ This is proved for Abelian varieties and Shimura varieties $X.$