### 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 SL_{3}. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for SL_{2}. Our conjectural construction would determine the exponents for SL_{3} WKB problems, and it can be put into practice on examples.

Original language | English (US) |
---|---|

Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 203-260 |

Number of pages | 58 |

Volume | 324 |

DOIs | |

State | Published - 2017 |

Externally published | Yes |

### Publication series

Name | Progress in Mathematics |
---|---|

Volume | 324 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Fingerprint

### 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

*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

**Constructing buildings and harmonic maps.** / Katzarkov, Ludmil; Noll, Alexander; Pandit, Pranav; Simpson, Carlos.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Progress in Mathematics.*vol. 324, Progress in Mathematics, vol. 324, Springer Basel, pp. 203-260. https://doi.org/10.1007/978-3-319-59939-7_6

}

TY - CHAP

T1 - Constructing buildings and harmonic maps

AU - Katzarkov, Ludmil

AU - Noll, Alexander

AU - Pandit, Pranav

AU - Simpson, Carlos

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - BPS state

KW - Building

KW - Grothendieck topology

KW - Polyhedral complex

KW - Spectral curve

KW - Spectral network

KW - WKB exponent

UR - http://www.scopus.com/inward/record.url?scp=85029432750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029432750&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-59939-7_6

DO - 10.1007/978-3-319-59939-7_6

M3 - Chapter

AN - SCOPUS:85029432750

VL - 324

T3 - Progress in Mathematics

SP - 203

EP - 260

BT - Progress in Mathematics

PB - Springer Basel

ER -