Quiver Donaldson-Thomas invariants are integers determined by the geometry of moduli spaces of quiver representations. I will describe a correspondence between quiver Donaldson-Thomas invariants and Gromov-Witten counts of rational curves in toric and cluster varieties. This is joint work with Pierrick Bousseau.

Anomalies in quantum systems are present when a classical symmetry is broken by quantum effects. They give rise to physical predictions and constraints. This talk will focus on the mathematical features of anomalies of continuous, ordinary, symmetries. In the first part, we will review the topological nature of anomalies, in particular the connection to the Atiyah-Singer index theorem and its non-perturbative path-integral computation by Fujikawa. We will then discuss how anomalies and their associated (topological) Chern-Simons polynomials are related to BRST cohomology via the Stora-Zumino chain of descent equations, explaining the connection to the two-step descent procedure reviewed in the talk by Alice Lüscher last term.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

I will present some contributions to the quasiisometry classification of solvable Lie groups of exponential growth that we obtain using sublinear bilipschitz equivalences, which are generalized quasiisometries. This is joint work with Ido Grayevsky.