June 05, 1990  June 05, 2023

Date:04WednesdayDecember 2019
Algebraic Geometry and Representation Theory Seminar
More informationTime  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 

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Details  Show 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 wellknown open rationality problem is the determination of a criterion for when a cubic hypersurface of fivedimensional 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 fulldimensional families of projective HyperKahler manifolds. Time permitting I'll discuss applications of the theory of relative stability conditions to problems other than cubic fourfolds.


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