4월3일(수) 17:00~17:50 5E102
연사:Raphaël Ponge (서울대)
제목: "Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry".
초록: A general goal of noncommutative geometry (in the sense of Alain Connes) is to translate
the main tools of differential geometry into the Hilbert space formalism of quantum mechanics
by taking advantage of the duality between spaces and algebras.
In this setting noncommutative spaces are represented through noncommutative algebras
that play formally the role of algebras of functions on these (ghost) noncommutative spaces.
As a result, this allows us to deal with a variety of geometric problems
whose noncommutative nature prevent us from using tools of classical differential geometry.
In particular, the Atiyah-Singer index theorem ultimately holds
in the setting of noncommutative geometry.