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.
|Titolo della pubblicazione ospite||Integrable Systems and Algebraic Geometry (vol. 2)|
|Editor||R Donagi, T. Shaska|
|Numero di pagine||45|
|Stato di pubblicazione||Pubblicato - 2020|
|Nome||LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES|
- Theta functions, Riemann surface braid groups, stable holomorphic vector bundles, prime form, Laughlin wave functions, noncommutative geometry, classical and quantum hamiltonian monodromy.