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In the last twenty years, many physical ideas, mostly borrowed from string theory, have led to deep mathematical results in geometry. Following this line of thought, we recently conjectured a new recursion structure in enumerative geometry, relying on physical insights from Random Matrix Theory, topological string theory and mirror symmetry. The recursion provides new formulae for the computation of generating functions in enumerative geometry, with many interesting ramifications. I will describe the recursion and sketch the main lines of the string theoretical framework underpinning our conjecture. Then I will outline a few of its mathematical implications in areas such as Gromov-Witten theory and Hurwitz theory.

There will be a colloquium dinner after the talk.