Homepage of Oscar Marmon

I am a postdoc at Lund University, funded by a scholarship from the Knut and Alice Wallenberg foundation. My research interest is number theory, more specifically studying the density of solutions to Diophantine equations using methods from algebraic geometry and analytic number theory.

• The density of integral points on complete intersections (with an appendix by Per Salberger)
  Q. J. Math. 59 (2008), 29-53. doi:10.1093/qmath/ham022
• The density of integral points on hypersurfaces of degree at least four.
  Acta Arith. 141 (2010), 211-240. doi:10.4064/aa141-3-1
• A generalization of the Bombieri-Pila determinant method.
  In Proceedings of the HIM trimester on Diophantine equations, Journal of Mathematical Sciences 171 (2010), 736-744.  doi:10.1007/s10958-010-0178-5 
• Sums and differences of four k-th powers.
  Monatsh. Math., 164 (2011), 55-74. doi:10.1007/s00605-010-0248-2
• The density of twins of k-free numbers (with R. Dietmann).
  Bull. London Math. Soc. 46 (2014), 818-826. doi:10.1112/blms/bdu038
• Random Thue and Fermat equations (with R. Dietmann).
  Acta Arith. 167 (2015), 189-200. doi:10.4064/aa167-2-6
• Diophantine equations in moderately many variables.
  Michigan Math. J. 65 (2016), 547-566. doi:10.1307/mmj/1472066147
• On the Hasse principle for quartic hypersurfaces (with P. Vishe).
  Duke Math. J.. 168 (2019), 2727-2799. doi:10.1215/00127094-2019-0025

• Where Geometry meets Number Theory, Gothenburg, July 17-19, 2017
• N³-Days IX, Lund, November 30-December 1, 2018
• Öresund Number Theory Day, Lund, January 28, 2020