@inbook{da1f0b788aa0498ba0e169e4a9a5e81c,

title = "Constructing buildings and harmonic maps",

abstract = "In a continuation of our previous work [21], we outline a theory which should lead to the construction of a universal pre-building and versal building with a ϕ-harmonic map from a Riemann surface, in the case of twodimensional buildings for the group SL3. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for SL2. Our conjectural construction would determine the exponents for SL3 WKB problems, and it can be put into practice on examples.",

keywords = "BPS state, Building, Grothendieck topology, Polyhedral complex, Spectral curve, Spectral network, WKB exponent",

author = "Ludmil Katzarkov and Alexander Noll and Pranav Pandit and Carlos Simpson",

note = "Funding Information: The authors were supported by an ERC grant, as well as the following grants: NSF DMS 0600800, NSF DMS 0652633 FRG, NSF DMS 0854977, NSF DMS 0901330, NSF DMS 150908, FWF P 24572 N25, FWF P20778, FWF P 27784-N25, ANR grant 933R03/13ANR002SRAR (Tofigrou), DMS-1265230 “Wall Crossings in Geometry and Physics”, DMS-1201475 “Spectra, Gaps, Degenerations and Cycles”, ERC Gemis, a Simons research grant, Simons collaborative Grant – HMS, OISE-1242272 PASI “On Wall Crossings, Stability Hodge Structures & TQFT”, and Advanced Grant “Arithmetic and physics of Higgs moduli spaces” No. 320593 of the European Research Council. LK was partially supported by the Laboratory of Mirror Symmetry NRU HSE, RF government grant, ag. 14.641.31.000. Funding Information: The authors would like to thank the University of Miami for hospitality and support during the completion of this work. The fourth named author would in addition like to thank the Fund For Mathematics at the Institute for Advanced Study in Princeton for support. The first named author was supported by the Simons Foundation as a Simons Fellow. Publisher Copyright: {\textcopyright} 2017 Springer International Publishing.",

year = "2017",

doi = "10.1007/978-3-319-59939-7_6",

language = "English (US)",

series = "Progress in Mathematics",

publisher = "Springer Basel",

pages = "203--260",

booktitle = "Progress in Mathematics",

}