Hi. I am Joseph Van Name. I am a Ph.D. student in mathematics at the University of South Florida. I work in areas including general topology(including uniform spaces and proximity spaces), point-free topology, lattice theory, Boolean algebras, universal algebra, and some set theory. I have related these areas using dualities that resemble Stone duality.
Expanded Research Statement:††††††††††††††
A Generalization of the Notion of a $P$-space to Proximity Spaces-This paper was recently accepted in the journal Topology Proceedings. This paper is easy to read.
V(Omega(A)) representations-This note contains a representation theorem for algebras in the variety V(Omega(A)). In particular, from this result, one can recover Keislerís theorem that represents complete elementary embeddings as limit ultrapowers.
Ultraparacompact Frame Duality (7/27/12, Mankato, Minnesota, Summer Conference on Topology and its Applications)-In this talk, I gave a duality between ultraparacompact frames and subcomplete locally refinable Boolean partition algebras. I have generalized this result since I gave this talk to a duality between all zero-dimensional frames and subcomplete Boolean covering algebras.
BPA-Ultrapowers(6/5/12, Bogota, Colombia, Latin American Symposium on Mathematical Logic)-This talk is about a very general ultrapower construction using Boolean partition algebras.
A Generalization of Stone Duality to Uniform Spaces(6/5/11, Lawrence, Kansas)-I this talk, I presented a duality between complete non-Archimedean uniform spaces and subcomplete stable Boolean partition algebras.
Pro-Filter Duality (USF discrete math seminar 11/05/12)-I started doing the research for this talk two weeks before the seminar.
LUB-systems (USF discrete math seminar 3/26/12)-In this talk, I start by giving well known results on closure systems. In the second half of this talk, I describe LUB-systems,admissibility systems, and LUB-based lattices. Since this talk I have extended the theory of LUB-systems considerably.
Boolean Partition Algebras and an Application to Ultrapowers(8/3/11, USF Discrete math seminar)-This is a talk for general mathematicians who do not specialize in logic.
Completeness and Representability in Boolean Algebras (2/14/11, USF Discrete math seminar)-
Large Cardinals and Point-Set Topology(UF Logic Seminar-11/30/10)-
http://mathoverflow.net -A place to ask and answer research level mathematics questions.
Spacebook-A database of topological spaces.
http://www.bible.is-Online Bible including audio in many languages.