Constructing Buildings and Harmonic Maps
Ludmil Katzarkov, Alexander Noll, Pranav Pandit, Carlos Simpson

TL;DR
This paper proposes a theoretical framework for constructing universal and versal buildings with harmonic maps from Riemann surfaces for the group SL_3, generalizing classical foliation theories and aiding in WKB problem analysis.
Contribution
It introduces a new theory for constructing universal pre-buildings and harmonic maps for SL_3, extending classical foliation concepts to higher-dimensional buildings.
Findings
Framework outlined for SL_3 harmonic maps
Potential to determine exponents in SL_3 WKB problems
Practical examples demonstrate the theory's application
Abstract
In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a -harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group . This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for . Our conjectural construction would determine the exponents for WKB problems, and it can be put into practice on examples.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics
