This is to announce the placement on the WWW of the notes of my two lectures at the Conference on Higher Category Theory and Mathematical Physics, Northwestern University (Evanston, Illinois; 28-30 March 1997). The site is: <www-math.mpce.mq.edu.au/~coact/street_nw97.ps> [I have tried to eliminate offending fonts and to accommodate funny US paper size. Thanks to Sjoerd Crans for helping here.] Title: The role of Michael Batanin's monoidal globular categories Lecture I: Globular categories and trees Lecture II: Higher operads and weak omega-categories This is a report on recent work of Michael Batanin. The goal of his work is to provide an environment for defining the concepts associated with weak omega-categories and for developing the ensuing theory. The approach is "globular". To put this in context, I might mention some important steps in the development of weak omega-categories. Categories were defined by Eilenberg-Mac Lane in 1945. Monoidal and symmetric monoidal categories were defined by Mac Lane in 1963. Ehresmann defined (strict) n-categories in 1966. B�nabou defined bicategories in 1967. In the early 80s, monoidal bicategories were in the air but a full definition was not published in that period. Joyal-Street defined braided monoidal categories in 1985. Gordon-Power-Street defined tricategories in 1991 (this, and the coherence theorem, were published in 1995). Braided monoidal categories were defined by Kapranov-Voevodsky-Baez-Neuchl-Breen around 1993. Trimble produced a definition of tetracategory in 1995. Diverse approaches to weak n-categories for all n have appeared. Street (1985) suggested a simplicial definition with horn filler conditions. Trimble (1994) approached the problem using operads and Stasheff associahedra. Baez-Dolan (1995) have a definition using typed operads and opetopes. Tamsamani (1996) gave a multisimplicial definition. Batanin uses higher operads and globular sets. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ross Street email: street@mpce.mq.edu.au Mathematics Department phone: +612 9850 8921 Macquarie University fax: +612 9850 8114 Sydney, NSW 2109 Australia Internet: http://www.mpce.mq.edu.au/~street/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~