Hilbert's 14th Problem and Cox rings -- Ana-Maria Castravet

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I will describe generators of the total coordinate ring of the blow-up of
P^n in any number of points that lie on a rational normal
curve. As a corollary, I will show that the algebra of invariants of an
action of the two-dimensional additive group introduced  by Nagata is
finitely generated by certain explicit determinants. The finite generation
of certain algebras of invariants of actions of additive groups related to
T-shaped Dynkin diagrams introduced by Mukai also follows. This is joint
work with E. Tevelev.