Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.

In the framework of an extended BRST formalism, it is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form (notoph) gauge theory presents an example of a tractable field theoretical model for the Hodge theory.

NOTICES OF THE AMS 335 I n late October and early November 1994 many mathematicians received e-mail from colleagues trumpeting the death of gauge theory. More than a decade earlier, S. K. Donaldson (Oxford) had found a deep but mysterious link between Yang-Mills theory from mathematical physics on the one hand and 4-dimensional differential topology on the other. Since then, many topologists ha...