Quantum Triangulations

Mauro Carfora, 19 received his Laurea in Physics from the University of Rome La Sapienza in 1977, and his PhD from University of Texas at Dallas in 1981. He has held positions at several Italian Universities and is a full professor of Mathematical Physics at the University of Pavia since 2001. Also, he has held visiting positions in universities and research institutions abroad, among which the University of California at Berkeley and Santa Barbara, USA, and the Nils Bohr Institute, Copenhagen, Denmark.His research interests include Geometrical Analysis, and Combinatorial methods in theoretical and mathematical Physics. Applications in quantum gravity and moduli space theory. Ricci flow on Riemannian manifolds. Applications of geometric flows to theoretical and mathematical Phyics. Renormalization group flow and geometrical flows. Relativistic cosmology. Annalisa Marzuoli received her Laurea in Physics in 1979. She held a research fellowship of the National Research Council inMathematical Physics from 1979-1984. Then she was a researcher in Theoretical Physics, until she became an associate professor in 2000, all at the University of Pavia.Her current fields of research include geometric and algebraic aspects of condensed matter systems (graphene and topological insulators) and of Topological Quantum Field Theories, with applications to quantum computing. Quantum integrable systems, their semiclassical analysis and relations with the Askey-Wilson scheme of hypergeometric orthogonal polynomials, with applications to atomic and molecular physics and to discretized gravity models. Improvement of interconnected algebraic, geometric and combinatorial methods to model many-body (quantum and lattice) systems.

• Preface.- Acknowledgements.- Triangulated Surfaces and Polyhedral Structures.- Singular Euclidean Structures and Riemann Surfaces.- Polyhedral Surfaces and the Weil-Petersson Form.- The Quantum Geometry of Polyhedral Surfaces: Non–Linear σ Model and Ricci Flow.- The Quantum Geometry of Polyhedral Surfaces: Variations on Strings and All That.- State Sum Models and Observables.- State Sum Models and Observables.- Combinatorial Framework for Topological Quantum Computing.- Appendix A: Riemannian Geometry.- Appendix B: A Capsule of Moduli Space Theory.- Appendix C: Spectral Theory on Polyhedral Surfaces.- Index.