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| About the cover: Rational curves on a K3 surface | |
| Curves: Rational points on curves | |
| Non-abelian descent and the generalized Fermat equation | |
| Merel's theorem on the boundedness of the torsion of elliptic curves | |
| Generalized Fermat equations (d'apres Halberstadt-Kraus) | |
| Heegner points and Sylvester's conjecture | |
| Shimura curve computations | |
| Computing Heegner points arising from Shimura curve parametrizations | |
| The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points | |
| Lectures on modular symbols | |
| Surfaces: Rational surfaces over nonclosed fields | |
| Non-abelian descent | |
| Mordell-Weil problem for cubic surfaces, numerical evidence | |
| Higher-dimensional varieties: Algebraic varieties with many rational points | |
| Birational geometry for number theorists | |
| Arithmetic over function fields | |
| Galois + Equidistribution = Manin-Mumford | |
| The Andre-Oort conjecture for products of modular curves | |
| Moduli of abelian varieties and $p$-divisible groups | |
| Cartier isomorphism and Hodge theory in the non-commutative case | |
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