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Wednesday, March 10, 2021

**Abstract:** Two important aspects of the structure of differential calculus are the chain and product rules. On manifolds, chain rule generalizes to the exterior derivative commuting with pullback by smooth maps. The product rule generalizes to a rule for the exterior derivative of wedge product of differential forms. These properties, especially the product rule, may be used as one of the defining properties for a covariant derivative in differential geometry. What if one is developing calculus and geometry for non-smooth spaces. One such application is the development of a discrete exterior calculus and discrete differential geometry for simplicial complexes (e.g. triangle meshes and tetrahedral meshes). What should play the role of the smooth maps, the exterior derivative, the wedge product and the covariant derivative so that we can speak of the above structural properties of calculus and geometry in this discrete setting? I will use examples to describe such a discrete calculus and geometry we have been developing. This will be a survey of some old ideas and some new developments. The newer developments are joint work with Mark Schubel (Apple Inc.) and Daniel Berwick-Evans (UIUC).

Monday, September 20, 2021

Friday, September 24, 2021

Monday, September 27, 2021