Two Approaches Towards Local Uniformization and Resolution of Singularities in Characteristic p > 0

Resolution of singularities is a very important tool in Algebraic Geometry. It is a modification of a singular variety X into a non-singular variety Y which shares many properties with X. A celebrated theorem of Hironaka, published in 1964, asserts that a resolution of singularities exists for a variety which is defined over a field of characteristic zero. In positive characteristic, the problem is widely open.
The aim of the summer school is to understand two recent results in the domain of resolution of singularities in positive characteristics: On the one hand, resolution of threefolds by Vincent Cossart and Olivier Piltant and on the other hand, local uniformization of Abhyankar valuations by toric morphisms which is due to Bernard Teissier.
A description of the school can be found on the link: sites.google.com/site/resolutionofsingularities/description