Equivariant Homotopy theory, that is, homotopy theory of spaces with an action of a specific group G, has been of great interest. One of the starting points of the subject was the spherical space form problem which was finally solved by Madsen, Wall and Thomas. The analogous statement for a product of spheres is one of the major unsolved problems in this subject called the rank conjecture. The techniques in equivariant homotopy theory also give a nice proof of the Atiyah-Segal completion theorem, among many other such results. These techniques are further carried forward in the relatively new topic in this area : Global homotopy theory which was introduced by Stefan Schwede.

The lecture series will present a rigorous formalism for global stable homotopy theory, and discuss examples of global homotopy types. The implementation uses the category of orthogonal spectra, with "global equivalences" as weak equivalences. Looking at orthogonal spectra through the eyes of global equivalences leads to a rich algebraic structure on equivariant homotopy groups, including restriction maps, inflation maps and transfer maps. Many interesting global homotopy types support additional ultra-commutative multiplications, and these gives rise to power operations that interact nicely with the other structure. The localization of orthogonal spectra at the class of global equivalences gives a tensor triangulated category much finer than the traditional stable homotopy category of algebraic topology."

The programme features lectures on global homotopy theory by Stefan Schwede while some necessary background on stable homotopy theory and equivariant homotopy theory will be covered by other participants.

Graduate students and postdoctoral fellows are especially encouraged to apply.