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How should we think about quantum computing? The usual answer to this question is based on ideas inspired by computer science, such as qubits, quantum gates, and quantum circuits. In this talk I will explain an alternate geometric approach to quantum computation. In the geometric approach, an optimal quantum computation corresponds to "free falling" along the minimal geodesics of a certain Riemannian manifold. This reformulation opens up the possibility of using tools from geometry to understand the strengths and weaknesses of quantum computation, and perhaps to understand what makes certain physical operations difficult (or easy) to synthesize.

The anatomy of a black hole.
Learning Outcomes:
• What are the mass requirements for a star to become a black hole?
• The anatomy of a Schwarzschild black hole, including the singularity and the event horizon.
• What a traveller would experience if he orbited a black hole, or had the bad luck to fall through the event horizon.

The physical attributes of a black hole and what types of physical evidence astronomers use the locate them.
Learning Outcomes:
• What are the physical requirements for a star to become a black hole, and what properties of that star remain after the black hole is formed?
• The types of black holes, including: the Schwarzschild black hole, the Reissner-Nordström black hole, the Kerr black hole, and the Kerr-Newman black hole.
• What a traveller would experience if he orbited one of these more general black holes, or fell through to the singularity.