Abstract: Given a 3d N=4 supersymmetric quantum field theory, there is an associated Coulomb branch, which is an important reflection of the A-twist of this theory. In the case of gauge theories, this Coulomb branch has a description due to Braverman-Finkelberg-Nakajima; I’ll discuss how we can generalize this geometric description in order to construct non-commutative resolutions of Coulomb branches (giving … Read More
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: We study the Borel summation of the Gromov-Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson-Thomas invariants of the resolved conifold, having a direct relation to the Riemann-Hilbert problem formulated by T. Bridgeland. There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative … 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
Abstract: I will present a particular set of 4d N=2 SCFTs that can be labeled with a pair of Lie groups of type ADE. For specific choices, we get infinitely many theories arising from this construction that have their two central charges to be identical: a=c (without taking any large N limit). Interestingly, the Schur indices of these theories are … Read More
Abstract: Mysterious duality was discovered by Iqbal, Neitzke, and Vafa in 2002 as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E_k. It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives … Read More
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on … Read More
Abstract: Quantum field theories and string theories often lead to perturbative series which encode geometric information. In this lecture I will argue that, in the case of complex Chern-Simons theory, perturbative series secretly encode integer invariants, related in some cases to BPS counting. The framework which makes this relation possible is the theory of resurgence, where perturbative series lead to additional … Read More