Theoretical and Mathematical Physics: Quantum Gravity and Quantum Field Theory
Among the many significant ideas and developments that connect Mathematics with contemporary Physics one of the most intriguing is the role that Quantum Field Theory (QFT) plays in Geometry and Topology. We can argue back and forth on the relevance of such a role, but the perspective QFT offers is often surprising and far reaching. Examples abound, and a fine selection is provided by the revealing insights offered by Yang--Mills theory into the topology of 4-manifolds, by the relation between Knot Theory and topological QFT, and most recently by the interaction between Strings, Riemann moduli space, and enumerative geometry. These techniques afford a geometrical perspective which is always quite non--trivial and extremely rich. It is within such a Quantum Geometry framework that our group (M. Carfora, A. Marzuoli, C. Dappiaggi) investigates aspects of the relation between an important class of QFTs, General Relativity, Cosmology, and Quantum Gravity. Specific research themes that we address and which offer a wide range of possibilities for master and PhD thesis are: Quantum Field Theory on curved spacetimes; Ricci flow and Quantum Field Theory Landscaping; Two-dimensional Quantum Gravity, String Dualities, and the geometry of Riemann Moduli Space theory; Topology of manifolds and Topological Quantum Field Theory; Combinatorial Framework for Topological Quantum Computing.
Staff: Mauro Carfora, Claudio Dappiaggi, Annalisa Marzuoli