PhD research topic - Domenico Fiorenza
Research areas
Topological quantum field theories
Keywords
Topological quantum field theories, symmetric monoidal categories, factorization algebras, elliptic cohomology, topological modular forms
Research topics
Topological quantum field theories are linear representations of (extended) cobordism. On the one hand they are a powerful source of algebraic invariants of manifolds (classical examples are the Jones polynomial, Turaev-Viro, and Dijkgraaf-Witten invariants). On the other hand, the intuition coming from the geometric nature of cobordism provides a clear explanation for otherwise mysterious algebraic constructions. An intriguing example is provided by elliptic cohomology. This is known in the physics folklore to be related to a certain supersymmetric quantum field theory, yet a rigorous construction remains elusive and an appealing challenge to mathematicians.
Bibliography
[1] Edward Witten, Elliptic Genera And Quantum Field Theory , Commun.Math.Phys. 109 525-536 (1987)
[2] Matthew Ando, Michael Hopkins, Neil Strickland, Elliptic spectra, the Witten genus, and the theorem of the cube, Inventiones Mathematicae, 146:595–687, 2001
[3] Stephan Stolz, Peter Teichner, What is an elliptic object? in Topology, geometry and quantum field theory , London Math. Soc. LNS 308, Cambridge Univ. Press (2004), 247-343
[4] P. Hu, I. Kriz, Conformal field theory and elliptic cohomology, Advances in Mathematics, Volume 189, Issue 2, 20 December 2004, Pages 325–412
[2] Matthew Ando, Michael Hopkins, Neil Strickland, Elliptic spectra, the Witten genus, and the theorem of the cube, Inventiones Mathematicae, 146:595–687, 2001
[3] Stephan Stolz, Peter Teichner, What is an elliptic object? in Topology, geometry and quantum field theory , London Math. Soc. LNS 308, Cambridge Univ. Press (2004), 247-343
[4] P. Hu, I. Kriz, Conformal field theory and elliptic cohomology, Advances in Mathematics, Volume 189, Issue 2, 20 December 2004, Pages 325–412