This is a brief introduction to the 2023 Polymath Jr project that will be run by Nathan Wagner.

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Our group will work on characterizing bounded Hankel operators on the Hartogs triangle. The Hartogs triangle is a domain in ℂ² which is a source of many counterexamples and interesting phenomena in complex analysis due to its non-smooth boundary, and Hankel operators act on spaces of holomorphic functions known as Bergman spaces. We will aim to find necessary and sufficient conditions to guarantee the boundedness of such operators in the case of the Hartogs triangle and with`respect to different norms. This project will be accessible to students who have studied some basic real analysis and complex analysis. A working knowledge of measure theory/Lebesgue integration is preferred but is not absolutely necessary. No experience with Bergman spaces, Hankel operators, or several complex variables is needed- we will spend the first couple weeks reviewing these topics.