Some Topological Applications of Theta Functions

Mauro Spera, 27408, BRESCIA - Dipartimento di Matematica e fisica 'Niccolò Tartaglia', FISICHE E NATURALI FACOLTA' DI SCIENZE MATEMATICHE, FISICHE E NATURALI FACOLTA' DI SCIENZE MATEMATICHE

Risultato della ricerca: Contributo in libroChapter

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteIntegrable Systems and Algebraic Geometry (vol. 2)
EditorR Donagi, T. Shaska
Pagine440-484
Numero di pagine45
Volume459
Stato di pubblicazionePubblicato - 2020

Serie di pubblicazioni

NomeLONDON 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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