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# Brent Pym, Special Colloquium

## December 4, 2017 @ 4:00 pm - 5:00 pm

**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.