MS Seminar (Mathematics - String Theory)

Speaker: Yalong Cao (Oxford U)
Title: Zero Dimensional Donaldson-Thomas Invariants of Calabi-Yau 4-folds
Date: Thu, Sep 20, 2018, 15:30 - 17:00
Place: Seminar Room A
Abstract: We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold X and define DT4 invariants by integrating the Euler class of a tautological vector bundle against the virtual class. We conjecture a formula for their generating series, which we prove in certain cases when L corresponds to a smooth divisor on X. A parallel equivariant conjecture for toric Calabi-Yau 4-folds is proposed. This conjecture is proved for smooth toric divisors and verified for more general toric divisors in many examples. Combining the equivariant conjecture with a vertex calculation, we find explicit positive rational weights, which can be assigned to solid partitions. The weighted generating function of solid partitions is given by exp(M(q)-1), where M(q) denotes the MacMahon function. This is joint work with Martijn Kool.
Remarks: Blackboard talk