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I am an undergrad (in math and econ) interested in pursuing a PhD in the latter. I can afford a pure math elective this semester and I am torn between diff geom and complex analysis. Which one is more useful for econ research (and for grad school apps)?

I am aware of sporadic but celebrated applications of diff geom (nonlinear estimators, arbitrage cones, for example), but I am struggling to find any for complex analysis.

PS: I took the usually recommended math classes— analyses 1 and 2, calc up to PDEs, etc— so 'neither is useful take X' isn't useful either :').

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It's very personal and no right answer, but I would go for Complex Analysis - it doesn't come up explicitly but it will be behind a lot of the time series results in econometrics and macro sequences if you want to learn the proofs properly. It also underlies a lot of continuous time stochastic analysis if you go into that area.

Tom Sargent was of the opinion that knowing complex analysis was an arbitrage opportunity as an academic economist - as an undergrad he told me to take it, but I took numerical optimisation instead and I still regret that decision.

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  • $\begingroup$ My economics background is only from self-study ( of macro ) but, As Debreu mentioned, complex analysis comes up a decent amount of time in advanced macro because solutions to differential equations ( and models in general ) sometimes involve it. I've never seen a macro application that required differential geometry but I'm not sure that I'd recognize it if I saw it. I'd go with complex analysis. $\endgroup$
    – mark leeds
    Nov 27, 2023 at 7:46

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