Hello, new to this board so sorry if i overlooked some formatting rules. I will be applying for grad school this year and am wondering what schools would be a 'reach' for my background.
I go to a mid-ranked Canadian university for my ug in mathematics, I have taken a handful of graduate and reading courses starting in my second year (PDEs, rep theory, algebraic topology). I currently have 2 papers published in Q1 journals (both substantial results for the topic), one of these papers was under a REU. My letters of recommendation are from people who are well known in their field (one has published a couple well-known books in his field, another visits IHES yearly and works/publishes with a very well known mathematician). With this in mind, what would be a reasonable tier of schools to apply too? I don't know how I stand compared to other students because I'm basically the only mathematically motivated undergrad at my school.
Also, I am still largely a self taught mathematician, how do I communicate that in my application? I've considered just reaching out to interesting profs and discussing their research but I'm not sure if that helps.
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