Benjamin Matschke , Rafael von Känel 

  • Elliptic curves with good reduction outside S
  • S-unit equation
  • Mordell equation
  • Cubic Thue equation
  • Cubic Thue–Mahler equation
  • Generalized Ramanujan–Nagell equation
  • Sums of units being a square or a cube
  • S-integral points on elliptic curves of given conductor
  • S-integral points on elliptic curves of high rank

References