Brent Pym, Special Colloquium

Title: Semi-classical and quantum projective geometry
Abstract: The idea that the abstract noncommutative algebras of quantum mechanics can be understood using geometric techniques and intuition is a pervasive theme in mathematics and physics.  In the 80s and 90s, Artin, Bondal, Kontsevich and others crystallized this philosophy of “noncommutative (or quantum) projective algebraic geometry” into a collection of inspiring problems and conjectures, many of which still remain open.  Recently, there have been several advances based on new insights into the “semi-classical limit”, where noncommutative rings are approximated by geometric spaces known as Poisson manifolds (the phase spaces of classical Hamiltonian mechanics).  I will give an overview of these developments, highlighting the roles played by an eclectic cast of characters, from spinning particles and elliptic curves, to moduli spaces and multiple zeta values.