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2020 international profile evaluation request

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Type of Student: International male
Undergrad Institution: Imperial College London (graduating June 2019)
Major: Mathematics
GPA: Expected high First Class (probably converts 3.8-4.0)
Mathematics Courses
Some of my courses were called slightly different things, but roughly in terms of standard US undergrad courses:
Calculus, Linear Algebra, Multivariable Calculus, Numerical Analysis, ODEs, Real Analysis, Complex Analysis, (point-set) Topology, Algebra,.
At perhaps upper level/early graduate (maybe? this seems to vary a lot looking at different places):
Measure Theory, Functional Analysis, (measure based) Probability, Analytic Methods in PDEs, Stochastic Calculus, Algebra, Differential Geometry, Algebraic Topology.
Statistics Courses
Not really sure when US students normally take most of these:
Probability and Statistics, Linear Models, Statistical Theory, Applied Probability, Time Series, Generalised Linear Models, Machine Learning.
Additional Info: One (applied) ML software engineering internship at a well known tech company. Will be working there after I graduate. Strong in Python, R, C++, Java.

GRE General Test:
V: 162
W: 4.5

GRE Subject Mathematics: 910 (97%)

Programs Applying: Statistics/Applied math
Research Experience: Implemented and studied the efficiency of some ML methods for a problem in astrostatistics over summer. Currently working on senior thesis about brownian motion on Riemannian manifolds (expository work).
Letters of Recommendation:  One from each of the research experiences, and one from a maths professor who knows me well.
Applying to Where: 
  • Stanford
  • Berkeley
  • Harvard
  • Chicago
  • Washington
  • Columbia
  • Yale

Applied math

  • UCLA
  • Caltech
  • NYU
  • Princeton
  • Cornell

And some places in the UK - haven't quite decided yet.

1. My grades weren't great in my first couple of years (just about on the Upper Second Class boundary) but went up significantly last year (to a high First) and should be similar this year. Due to heavier weighting in later years, my final degree classification will be fine, as I am doing well in my upper level/graduate coursework, but my transcript will show weak marks in a lot of the undergrad courses. Are not-fantastic grades on Real Analysis a big deal if I've done a great job on Measure/Functional/PDEs/Stochastics etc?
2. My letter recommenders aren't particularly well known. I know in Mathematics PhD admissions, by far the most important part of an application to strong schools is having excellent recommendations from professors who are known to the departments you're applying to. Is this also the case for Statistics?
3. Is spending time in industry frowned upon? I wanted to delay applications just one year to apply with a stronger averaged grade and having completed my senior thesis.
4. I suppose all concerns really point to this last one in most posts like this - am I being overly ambitious?
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I think you have a very good shot at some of the schools you listed, but it's a very top-heavy list (for both statistics and math -- NYU Courant and UCLA are basically two of the best applied math schools in the world, and NYU and Princeton are even more competitive to get into than Stanford of UCB Statistics). Competition for international applicants tends to be particularly fierce, so it might be a gamble to apply to *only* those schools. I would suggest applying to a few "safer bets." WIth your profile, you probably don't need to apply much lower than NCSU or UMich for Statistics or University of Maryland-College Park for Applied Math.

As for your concerns:

1) If you're finishing in the high first class at Oxbridge/ICL, I think you're golden. 

2) It is more important that the letters be strong and say things like how you were one of the best students they've taught in years than that the letter writers be well-known. Well-known recommenders who have connections may matter more in fields like computer science or physical sciences where students are recommended for acceptance by a PI (so obviously, a letter from a collaborator of the PI would look great). But in Statistics and Mathematics, admissions decisions are made by the department, and PhD students are not accepted into PI's labs. 

3) I think adcoms are generally neutral about industry experience (doesn't tend to hurt or help the application). There are PhD alumni and students at UC Berkeley who have started their PhD over 10 years after they graduated undergrad.

4) See first paragraph.

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