Jack Carlisle

The subject of G-equivariant homotopy theory has become ubiquitous in modern mathematics. In this field, one studies G-equivariant cohomology theories, which are represented by G-spectra. There are G-equivariant analogues of ordinary cohomology, K-theory, and complex cobordism, to name a few. Just as in the non-equivariant case, complex oriented G-spectra play an important role in equivariant homotopy theory. This is because of the deep connection between complex oriented G-spectra and G-equivariant formal group laws, which has been developed extensively over the past several decades. A primary goal of my research is to further understand this connection from a calculational and theoretical perspective. In addition to this primary interest, I am interested in foundations of equivariant algebra, the Hurwitz realizability problem for branched covers of Riemann surfaces, and various topics in low dimensional and geometric topology.