A ubiquitous and powerful concept in mathematical physics is that of dualities. Two theories which may be describing very different physics are said to be dual if there is a non-trivial equivalence between them. An important class of dualities relates theories of classical physics to theories of quantum physics. I will give an introduction to the "ODE/IM correspondence" which provides remarkable examples of such classical/quantum dualities in the context of integrable (exactly solvable) field theories.

The talk should be suitable for undergraduates with familiarity with basic number theory, algebra and analysis.

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