Something from Nothing

This piece of art, made by Jeremiah Heller, is a true fairytale taking place in K-theory Wonderland! More about this video: Math prerequisites: zeroth algebraic K-theory Math summary of the video: K-theory of a ring is defined as the group completion of the monoid of its finitely generated projective modules. If you take all projective modules, not just finitely generated, then the group completion of this bigger ring turns out to be zero. At the core of this, is a technique which leads to a definition of negative K-theory groups of a ring. Negative K-theory vanishes for smooth varieties, but it gives us new interesting invariants of varieties with singularities! Jeremiah’s webpage: Interview with Jeremiah Heller and Vesna Stojanoska: Music is the courtesy of: