I work in algebraic geometry, specializing in the study of singularities and birational geometry of algebraic varieties and the structure of arc spaces and other valuation spaces. Other areas of interest include rationality of algebraic varieties, Cremona groups, Fano varieties, motivic integration, non-archimedean geometry, multiplier ideals, and positivity in algebraic geometry
Research to which I have contributed has been featured in the following articles:
- B. Totaro,
The ACC conjecture for log canonical thresholds [after de Fernex, Ein, Mustata, Kollár],
Séminaire Bourbaki, Juin 2010, 62éme année, 2009-2010, no. 1025
- J. Kollár,
The rigidity theorem of Fano–Segre–Iskovskikh–Manin–Pukhlikov–Corti–Cheltsov–de Fernex–Ein–Mustata–Zhuang,
in Birational Geometry of Hypersurfaces, Gargnano del Garda, Italy, 2018,
Lecture Notes of the Unione Matematica Italiana, Vol 26, Springer, 2019
- M. Lejeune-Jalabert,
The algebraic answer to the Nash problem for normal surfaces according to de Fernex and Docampo,
in Arc Schemes and Singularities, World Scientific Publishing, 2019
- M. Mauri,
The dual complex of singularities after de Fernex, Kollár and Xu ,
in Arc Schemes and Singularities, World Scientific Publishing, 2019
research partially suppported by the National Science Foundation