December 10, 1989 - December 10, 2022

  • Date:04WednesdayDecember 2019

    Algebraic Geometry and Representation Theory Seminar

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    Time
    09:30 - 10:45
    Title
    Cubic Fourfolds: Rationality and Derived Categories
    Location
    Jacob Ziskind Building
    Room 1
    Lecturer
    Howard Nuer
    University of Illinois at Chicago
    Organizer
    Faculty of Mathematics and Computer Science
    Seminar, Department of Computer Science and Applied Mathematics
    Seminar, Department of Mathematics
    Seminar
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    DetailsShow full text description of The question of determining if a given algebraic variety is ...»
    The question of determining if a given algebraic variety is rational is a notoriously difficult problem in algebraic geometry, and attempts to solve rationality problems have often produced powerful new techniques. A well-known open rationality problem is the determination of a criterion for when a cubic hypersurface of five-dimensional projective space is rational. After discussing the history of this problem, I will introduce the two conjectural rationality criteria that have been put forth and then discuss a package of tools I have developed with my collaborators to bring these two conjectures together. Our theory of Relative Bridgeland Stability has a number of other beautiful consequences such as a new proof of the integral Hodge Conjecture for Cubic Fourfolds and the construction of full-dimensional families of projective HyperKahler manifolds. Time permitting I'll discuss applications of the theory of relative stability conditions to problems other than cubic fourfolds.
    Lecture