Mathematics Colloquia and Seminars

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There is a project (due to Andrey Losev) of constructing "exact discretizations" of topological quantum field theories by fiber Batalin-Vilkovisky integral. The discretized theory lives on a triangulated manifold and has a finite dimensional space of fields, but features the same partition function as the continuum theory. We will discuss two explicit examples where this program was carried out: the BF theory in arbitrary dimension, and 1-dimensional Chern-Simons theory. The latter example can be stated as Atiyah's TQFT living on triangulated 1-cobordisms, with partition function satisfying a version of BV quantum master equation with boundary terms (as a reminder of the gauge symmetry of the continuum theory).