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I am a postdoc currently on the academic job market who does interdisciplinary work. My phd is in mathematical physics, granted by a physics department, while working with a research group technically within a computer science department. I do work in quantum computation and lean heavily towards mathematics, unlike many researchers in QC. I publish in all of mathematics, physics, and computer science. There is a body of mathematical knowledge lacking in the topic that I study and, therefore, I work on both building and exploiting the necessary math from the ground up.

I'm reworking my research statement and will be applying to positions in all of mathematics, physics, and computer science. Should I be writing different research statements targeted at each department or will one statement that summarizes my overarching project suffice? Also, will describing myself as a mathematical physicist (as opposed to a mathematician or computer scientist) hurt me when applying to jobs outside of physics proper.

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What you write should depend in part on the type of job and the type of institution you are applying for.

To apply for a research focused position in a high level research institution, your statement should reflect something about your suitability to work with them explicitly. So different statements for different institutions would be warranted in that case. Each with a different focus, but also showing how your other interests support your work in that primary field.

For a more general position, say one that involves as much teaching as research, or the research requirements are more "casual", a general statement would probably be better as it shows flexibility that the institution might value.

But in general, make it about how you fit the needs of the position.

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