His past research activities have explored: topological Quantum Field Theories in any dimension, BF theories, Cohomology of imbedded loops, Higher dimensional knots; Links, knots and quantum groups; Differential geometrical aspects of string and field theories, Virasoro and Krichever-Novikov algebras; Anomalies in Quantum field theory and their differential geometrical interpretation; and Foundational aspects of Quantum Mechanics.
Cohomology | cohomology |
University of Rome and in 1975 a Ph.D. from the University of Warwick under the supervision of George Lusztig (The mod-2 Cohomology of the orthogonal groups over a finite field).
Taking the direct limit of these groups and inclusions yields the stable mapping class group, whose rational cohomology ring was conjectured by David Mumford (one of conjectures called the Mumford conjectures).
He is known for his work on norm varieties (a key part in the proof of the Bloch-Kato conjecture) and for the Rost invariant (a cohomological invariant with values in Galois cohomology of degree 3).
Its development was rapid in the years after 1950, when it was realised that sheaf cohomology was connected with more classical methods applied to the Riemann-Roch theorem, the analysis of a linear system of divisors in algebraic geometry, several complex variables, and Hodge theory.
Using the superconnection formalism of Quillen, they obtained a refinement of the Riemann–Roch formula, which links together the Thom classes in K-theory and cohomology, as an equality on the level of differential forms.