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Math-Physics Joint Seminar

Tuesday, September 27, 2022 - 3:30pm

Quincy Frias

George Mason University

Location

University of Pennsylvania

DRL 4C6

the seminar is postponed until October 18, 2022

Smooth manifolds can be described by their ring of smooth real-valued functions, in a similar way to an affine variety. However, this ring has much more structure which is captured in an algebraic gadget called a $C^\infty$ ring. Recently, work in derived differential geometry has led to notions of derived manifolds that arise out of variations on $C^\infty$ rings, as in Dr. Dominic Joyce's work. It was recently shown that dg-$C^\infty$ rings form the backbone for a proper $\infty$-category of derived manifolds. This series of talks will cover the connection between a suitable truncation of this $\infty$-category, made up of groupoids in $C^\infty$ rings, and the 2-category of d-manifolds.