Abstract by Zachary Hacking
Shortcuts in Diophantine Approximations, Part 2
This is the second half of a talk that discusses Diophantine approximations and improvements to them as outlined by Dirichlet's approximation theorem and subsequent results. In this half, we reframe the problem of approximation as finding points within a lattice defined by the target irrational. We show how this method helps in generating good approximations by introducing the L^p unit ball. We conjecture about how even better approximations may be generated by adjustments to this method.