algebraicgeometry arithmeticalalgebraicgeometry arithmeticalgebraicgeometry(diophantinegeometry) arithmeticvarietiesandschemes;arakelovtheory;heights curvesofarbitrarygenusorgenus$\ne1$overglobalfields evolutionequations geometry hamilton-jacobiequations numbertheory othergeneralizations parabolicdifferentialequations potentialsandcapacities potentialtheory rationalpoints settheory