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Buildings, spectral networks, and the Riemann-Hilbert correspondence at infinity

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 14, 2015 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Pranav Pandit (International Centre for Theoretical Sciences)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • folations - leaves

  • universal covers of Riemann surface

  • Kontsevich-Soibelman deformation theory

  • Derived Algebraic Geometry

  • wall-crossing formula

  • stability conditions

  • Fukaya category

  • WKB theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14220

Abstract

I will describe joint work with Katzarkov, Noll, and Simpson, which introduces the notion of a versal harmonic map to a building associated with a given spectral cover of a Riemann surface, generalizing to higher rank the leaf space of the foliation defined by a quadratic differential. A motivating goal is to develop a geometric framework for studying spectral networks that affords a new perspective on their role in the theory of Bridgeland stability structures and the WKB theory of differential equations depending on a small parameter. This talk will focus on the WKB aspect: I will discuss the sense in which the asymptotic behavior of the Riemann-Hilbert correspondence is governed by versal harmonic maps to buildings. 

Supplements
23392?type=thumb Pandit.Notes 498 KB application/pdf Download
Video/Audio Files

14220

H.264 Video 14220.mp4 387 MB video/mp4 rtsp://videos.msri.org/data/000/023/281/original/14220.mp4 Download
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