MS Seminar (Mathematics - String Theory)

Speaker: Ben Davison (U of Glasgow)
Title: Cohomological BPS invariants, vanishing cycles and Kac-Moody Lie algebras.
Date (JST): Mon, Apr 10, 2017, 13:15 - 14:45
Place: Seminar Room A
Abstract: The theory of Donaldson-Thomas invariants associates to a quiver Q with potential W a partition function recording the weight polynomials of the cohomology of moduli stacks of representations built out of the Jacobi algebra associated to Q and W. This theory is a local model for the category of coherent sheaves on a Calabi-Yau 3-fold. While the partition function looks wildly infinite, after taking plethystic logarithms and multiplying by (1-q) it becomes a power series with polynomial coefficients - the so-called refined DT invariants. I will explain how to lift these invariants from polynomials to mixed Hodge structures, via categorification, and how this allows us to define a natural Lie algebra associated to an arbitrary quiver, extending the Kac-Moody Lie algebra of the quiver, that conjecturally is the geometric Yangian defined by Maulik and Okounkov.