Boyer, Gordon, and Hu proposed a relative version of the L-space conjecture using slope detections and conjectured that this should be equivalent to the L-space conjecture for toroidal manifolds. We establish the equivalence for the foliation-detection part.

Abstract: The famous Aharonov–Bohm effect demonstrates the non-trivial quantum mechanical effect of (singular) magnetic potentials. Although the single pole case has been studied widely using rotational and scaling invariance, the technique fails to work for the Aharonov–Bohm Hamiltonian with multiple poles. In this talk, we will discuss a new framework to study the resolvent, resonances, and wave asymptotics of the Aharonov–Bohm Hamiltonian with multiple poles. This results in an interesting behavior where scattering and wave asymptotics depend on the magnetic fluxes, interpolating the odd and even dimensional Euclidean scattering. This talk includes joint works with Tanya Christiansen and Kiril Datchev. 

Representation theoretic multiplicities are at the heart of many open
problems in algebraic combinatorics. At the same time these
quantities appear in Geometric Complexity Theory in the search for
multiplicity obstructions for separating computational complexity
classes like VP vs VNP. Most recently they have also been considered
in quantum computing.
In this talk we will introduce the objects and problems, explain how
formalization through computational complexity theory could answer
some of the open problems in the negative. We will also explain their
role in GCT and quantum computing with a mixture of positive and
negative answers.