Quantum computation
==================
You can hardly open the newspaper nowadays without seeing something about Quantum computation. But aside from the hype and the industry interest, this deceivingly simple model offers a surprisingly rich set of mathematical, physical and conceptual questions, which seem to touch upon almost any area of mathematics: from group representations, to Markov chains, Knot invariants, expanders, cryptography, lattices, differential geometry, and many more.
I will give some definitions, provide some basic results, and sketch some open problems.