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Quantum many body physics in single and bilayer graphene

I discuss various quantum many body states that can arise in graphene based systems. To observe many body physics in graphene, it is essential to get around the vanishing density of states, which suppresses interaction effects. I discuss three methods of realizing many body physics in graphene. Doping graphene to a Van Hove singularity in the density of states can allow us to realize numerous exotic states, including chiral superconductors and unusual magnetic and pseudogap states. Meanwhile, bilayer graphene has a strongly ordered ground state even in the absence of any doping. I will discuss the nature of this ground state and how it may be probed experimentally. Finally, I discuss the unusual many body physics that arises in graphene in the quantum Hall regime.