TY - CHAP

T1 - Some Topological Applications of Theta Functions

AU - Spera, Mauro

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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

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

UR - http://hdl.handle.net/10807/149955

M3 - Chapter

SN - 9781108715775

VL - 459

T3 - LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES

SP - 440

EP - 484

BT - Integrable Systems and Algebraic Geometry (vol. 2)

A2 - Donagi, R

A2 - Shaska, T.

ER -