[8] In 2008, Carlsson cofounded Ayasdi, a predictive technology based on big data, machine learning and artificial intelligence.

Building on earlier work by Frank Adams, Jeremy Gunawardena, Haynes Miller, J. Peter May, James McClure, and L. Gaunce Lewis, Carlsson proved this conjecture in 1982.

He also adapted the techniques to provide a proof of Sullivan's fixed point conjecture, which was also proved simultaneously and independently by Miller and Jean Lannes.

Algebraic K-theory is a topological construction that assigns spaces (ultimately spectra) to rings, schemes, and other non-topological input.

This work is central to the development of tools by Ayasdi, Inc, for analyzing massive and complex data sets across multiple application domains.