Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture these rank 1 … Read More

Abstract: Over the past decade we have witnessed the emergence of a plethora of correspondences between QFTs in various dimensions arising from higher dimensional SCFTs. In this talk I will overview another strategy (well-known to experts) to obtain correspondences building upon geometric engineering techniques. Several new applications and examples will be presented, involving supersymmetric theories in different dimensions. In particular, we will include … Read More

Abstract: The Reshetikhin-Turaev construction for the quantum group U_q(gl(1|1)) sends tangles to C(q)-linear maps in such a way that a knot is sent to its Alexander polynomial. Tangle Floer homology is a combinatorial generalization of knot Floer homology which sends tangles to (homotopy equivalence classes of) bigraded dg bimodules. In earlier work with Ellis and Vertesi, we show that tangle … Read More