Kim Williams is the director of the successful, ongoing conference series, "Nexus: Relationships Between Architecture and Mathematics." When she first began writing about architecture and mathematics in 1988, there was no specific venue for the publication of scholarly studies regarding the relationships of architecture to geometry, theories of proportion, number symbolism and the like. The Nexus conferences began in 1996, along with the book series, "Nexus: Architecture and Mathematics". The first three conferences were held in Italy, in Fucecchio (1996), Mantua (1998), Ferrara (2000). In 2002, the first Nexus conference outside of Italy was held in Obidos, Portugal. Nexus 2004 took place in Mexico City. Nexus 2006 brought Nexus once again to Italy, and took place in Genoa in June 2006. Nexus 2008 took place in San Diego, California. Nexus 2010 will take place in Porto, Portugal. The conferences attract an international following of architects and mathematicians, but also historians, scientists, archaeologists and theologians.

The response to the biennial conferences was so great that in 1999 Kim Williams founded the Nexus Network Journal, a peer-reviewed journal for mathematics and mathematics. The NNJ is published both in electronic form and in print. As of January 2006, the NNJ is co-published by Kim Williams Books and Birkhauser Publishers of Basel, Switzerland.

In 2000 Kim Williams Books was founded to publish full-length studies and monographs. Based on her experience publishing the Nexus books and the Nexus Network Journal, Kim Williams is able to publish scholarly books of the highest quality, based on careful peer-review and editing, and printing and binding using the latest technology and fine paper stocks and binding.

The on-going Nexus conference and book series has given rise to a unique opportunity not only to present studies in a given discipline, but actually to give form to that discipline.