Some Topological Applications of Theta Functions

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper some recent topological applications of Riemann surface theory and especially of their associated theta functions (in different geometric incarnations) are surveyed, taking the circle of ideas around geometric quantization as a vantage point. They include classical and quantum monodromy of 2d-integrable systems and the construction of unitary Riemann surface braid group representations (aimed, in particular, at devising a mathematical interpretation of the Laughlin wave functions emerging in condensed matter physics). The noncommutative version of theta functions due to A. Schwarz is briefly discussed, showing in particular its efficacy in Fourier-Mukai-Nahm computations.
Original languageEnglish
Title of host publicationIntegrable Systems and Algebraic Geometry (vol. 2)
EditorsR Donagi, T. Shaska
Pages440-484
Number of pages45
Volume459
Publication statusPublished - 2020

Publication series

NameLONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES

Keywords

  • Theta functions, Riemann surface braid groups, stable holomorphic vector bundles, prime form, Laughlin wave functions, noncommutative geometry, classical and quantum hamiltonian monodromy.

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