revealed by high-magnetic fields*

A paradigm of unconventional superconductivity invoked for the cuprates is that the unusually high superconducting temperatures is caused by strong electronic interactions near a zero temperature phase transition termed a quantum critical point (QCP). We report measurements of the low temperature electronic structure of the single-layer cuprate featuring the highest superconducting temperatures, HgBa₂CuO_4+δ (Hg1201). Quantum oscillations indicate that the Fermi surface is comprised of only a single quasi-two dimensional pocket that likely results from Fermi-surface reconstruction by a charge density wave order. High magnetic field measurements up to 90 T allow us to determine the boundaries of this order and identify two putative quantum critical points. Measurements of the doping dependent effective mass and upper critical fields provide additional support for strong-correlations around these QCPs.