Mathematical Homepage of Oscar Marmon

My research interest is number theory, primarily 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
• Rational points close to non-singular algebraic curves (with F. Adiceam).
  To appear in Mathematika . arXiv:2204.11607

• 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
  
• Hausdorff School The Circle Method, HCM Bonn (online), May 10-21, 2021