Constructing buildings and harmonic maps

Ludmil Katzarkov, Alexander Noll, Pranav Pandit, Carlos Simpson

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages203-260
Number of pages58
Volume324
DOIs
StatePublished - 2017
Externally publishedYes

Publication series

NameProgress in Mathematics
Volume324
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

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Keywords

  • BPS state
  • Building
  • Grothendieck topology
  • Polyhedral complex
  • Spectral curve
  • Spectral network
  • WKB exponent

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Katzarkov, L., Noll, A., Pandit, P., & Simpson, C. (2017). Constructing buildings and harmonic maps. In Progress in Mathematics (Vol. 324, pp. 203-260). (Progress in Mathematics; Vol. 324). Springer Basel. https://doi.org/10.1007/978-3-319-59939-7_6