Gordan Savin
University of Utah, Salt Lake, USA
December 31, 2009
Geometry of binary hermitian forms: In a remarkable booklet `The sensual (quadratic) form', J. H. Conway introduces an elegant approach to integral binary quadratic forms. The main tool is a 3 valence tree which is in fact an SL$_2(Z)$-equivariant retract of the 2-dimensional hyperbolic space.Let $A$ be the ring of integers of a quadratic imaginary extension of the field of rational numbers. The 3-dimensional hyperbolic space has a 2-dimensional, GL$_2(A)$-invariant retract. The retract is a CAT(0) complex. In this lecture I will explain how the retract can be used to derive some results on hermitian binary forms over the ring $A$.
This is a joint work with Mladen Bestvina.
University of Utah, Salt Lake, USA
December 31, 2009
Geometry of binary hermitian forms: In a remarkable booklet `The sensual (quadratic) form', J. H. Conway introduces an elegant approach to integral binary quadratic forms. The main tool is a 3 valence tree which is in fact an SL$_2(Z)$-equivariant retract of the 2-dimensional hyperbolic space.Let $A$ be the ring of integers of a quadratic imaginary extension of the field of rational numbers. The 3-dimensional hyperbolic space has a 2-dimensional, GL$_2(A)$-invariant retract. The retract is a CAT(0) complex. In this lecture I will explain how the retract can be used to derive some results on hermitian binary forms over the ring $A$.
This is a joint work with Mladen Bestvina.