I am Joseph Van Name, and I have recently joined Booles’ Rings. I currently know several of the people here on Booles’ Rings through either mathoverflow.net or through the New York City logic community. I enjoy reading the mathematical posts here on Booles’ rings, and I am glad to be a part of this community.
I have requested to join Booles’ Rings in part due to my recent research endeavors towards understanding Laver tables. Through Booles’ Rings, I intend to post data, images, computer programs, and of course short mathematical expositions about these generalizations of the notion of a Laver table. Of course, I will also make posts about other areas of mathematics that I have researched in the past including publications and notes and slides for past talks. I therefore plan on having two portions of my site with one portion containing all the information on Laver tables one could ask for while the other portion is about all my other research projects.
Hopefully, through Booles’ Rings, I will use generalizations of Laver tables to establish a much needed common ground between set theory (in particular large cardinals) and structures such as self-distributive algebras, knots, braids and possibly other areas. By relating large cardinals to more conventional areas of mathematics, I intend to help non set-theorists see large cardinals not as being irrelevant objects that lie high above the clouds but as objects of a practical importance despite their astonishing size.
In the past, I have researched Stone duality which relates various fields of mathematics together including general and point-free topology, set theory (in particular the category of filters and Boolean-valued models), category theory, Boolean algebras, and more generally ordered sets, and a few other areas. However, since July of 2015, I have been researching generalizations of the notion of a Laver table. I would say that I have been more or less an applied set theorist (whatever that means) at least for most of the past year.
I have graduated from the University of South Florida in May of 2013. However, since the University of South Florida did not have a practicing logician, I was completely on my own in my research and I had to guide and formulate my own research myself. Fortunately, through my work on Stone duality, I was able to appreciate different areas of mathematics and relate these diverse areas of mathematics to each other. I currently reside in the New York City metropolitan area and am a part of the New York City mathematical logic community.