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We develop parallel transport on path spaces from a differential geometric approach, whose integral version connects with the category theoretic approach. In the framework of 2-connections, our approach leads to further development of higher gauge theory, where end points of the path need not be fixed., Comment: 6 pages, 2 figures. Talk delivered by S. Chatterjee at XXVIII WGMP, 28th June-4th July, 2009. Bialowieza, Poland

We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework., Comment: 27pp 3fig pdflatex only; v2: rewritten with several clarifications; v3: minor changes, added references. Version to be published, 30pp

We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects., Comment: 16 pages, presented at a conference titled Stochastic Analysis and Mathematical Physics 2006, organized by Ana Bela Cruzeiro and Jean-Claude Zambrini

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces., Comment: 12 pp.; the Introduction has been rewritten and mention of cohomology dropped in Proposition 3.2; material slightly reorganized