Homotopy Theory for Coalgebras 

We investigate how to use homotopy-theoretical methods in order to study coalgebras, using model categories and \$\infty\$-categories. We explain how model categories fail to represent the correct homotopy theory of coalgebras in spectra, from joint work with Brooke Shipley. If time permits, we will also explore current progress in understanding the \$\infty\$-category of \$A_\infty\$ coalgebras over the Eilenberg-Mac Lane spectrum of a field.