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.

### Math-Physics Joint Seminar

Tuesday, September 27, 2022 - 3:30pm

#### Quincy Frias

George Mason University