Quantum Oscillations in underdoped YBCO: the nature of Fermi surface reconstruction and evolution toward the Mott insulating regime

I will present results of quantum oscillation measurements we have measured in underdoped YBCO$_{6+x}$ that reveal a small Fermi surface. Results of angular dependent measurements enable us to obtain clues as to the nature of order that reconstructs the Fermi surface. I will also present results of doping-dependent measurements that enable us to trace Fermi surface evolution as the insulating regime is approached. \vspace{4 mm} Work was performed in collaboration with N. Harrison, G. G. Lonzarich, C. Mielke, R. Liang, D. Bonn and W. Hardy