Which US schools can I hope to be admitted to for a PhD?

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FrodCube
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Hi. I'm an international student from a pretty good italian university and I'm applying for a PhD in the US. Here's my profile:
  • 930 (89%) PGRE
  • 159v, 164q, 3.5w GRE
  • Still waiting for the TOEFL, but should be good
  • 4.0 GPA
  • 3 letters, hopefully good but how can I know? One is a decently known HEP theorist, who even spent some time at MIT.
Also since I'm italian, I have a 3 years "basic" degree and I'm currently taking the 2 year "specialization" degree in Theoretical Physics where I've taken/I'm taking GR, QFT, Cosmology, Many Body Physics and an introduction to Standard Model classes. I should get this degree in July or early September.

I don't really have any real research experience, but I will start working on a project about Force Free Electrodynamics and Black Holes in a month or less that should take about 6 months and could also imply a small collaboration with the Niels Bohr Institute in Copenaghen.

What would I like to do? If I had to answer with what I'd really like to study I'd say theoretical HEP, but I know that this is a very competitive subject and there's plenty of people with a better profile then mine.

So far I'm applying to: MIT, Harvard, Berkeley and Stanford. Since before taking the test they ask you to select 4 free score recipients I've decided to go with the top names in the field.

Here's my questions:

  1. Given my profile, which schools should I apply to? I'm interested in top-ish tier programs.
  2. Should I change my research interest to give me a higher chance of admission?
 
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You're applying to the top schools even though you have "no real research experience?" You might want to throw in some safety schools.