GPA: 90% (top 3 in the year, i.e. 200 maths students)
Type of student: EU national
GRE: haven't taken yet (90+ percentile should not be a problem in quant and subject test)
TOEFL: haven't taken yet
Program Applying: Pure Maths (possibly also some financial maths ones)
Research Experience: one supper project in regularity theory for elliptic PDE.
Others: 2 brozes italian maths olympiads, one of my rec letters will be from a prof that is quite well known in the analysis research world, who said that he would be happy to take me as phd student in his centre, the other references are from not very famous people.
Should I even bother trying to apply to top 5/10 US programs?
Thank you very much!