June 05, 1990 - June 05, 2023

  • Date:04WednesdayDecember 2019

    Algebraic Geometry and Representation Theory Seminar

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    09:30 - 10:45
    Cubic Fourfolds: Rationality and Derived Categories
    Jacob Ziskind Building
    Room 1
    Howard Nuer
    University of Illinois at Chicago
    Faculty of Mathematics and Computer Science
    Seminar, Department of Computer Science and Applied Mathematics
    Seminar, Department of Mathematics
    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.