A Riemann–Hilbert problem for uncoupled BPS structures

  • Anna BarbieriEmail author
Open Access


We study the Riemann–Hilbert problem attached to an uncoupled BPS structure proposed by Bridgeland in (“Riemann–Hilbert problems from Donaldson–Thomas theory I”). We show that it has “essentially” unique meromorphic solutions given by a product of Gamma functions. We reconstruct the corresponding connection.

Mathematics Subject Classification

14 30D 33B15 45Q05 



The author is grateful to Tom Bridgeland for many interesting discussions. Thanks are also due to Dylan Allegretti, Jacopo Stoppa (and the anonymous referee) for their comments on the preliminary version. The research leading to these results has received funding from the European research council.


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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of MathematicsUniversity of SheffieldSheffieldUK

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