Badly approximable vectors, $C^{1}$ curves and number fields
  We show that points on $C^{1}$ curves which are badly approximable by rationals in a number field form a winning set in the sense of W. M. Schmidt. As a consequence, we obtain a number field version of Schmidt's conjecture. 
Manfred Einsiedler, Anish Ghosh, Beverly Lytle
math.DS