Abstract Zhen Huan

Zhen Huan will speak on

Quasi-elliptic cohomology

Abstract: Quasi-elliptic cohomology is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most ellipitc cohomology theories. Quasi-elliptic cohomology is closely related to Tate K-theory. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. Moreover, we construct a G-orthogonal spectrum weakly representing quasi-elliptic cohomology. This construction leads to the birth of a new global homotopy theory.