DubTop Seminar: (A synthetic approach to detecting) v1-periodic families

The stable homotopy groups of spheres are hard to calculate. Chromatic homotopy theory offers an organizational principle to sort the elements of these groups into periodic layers. Adams constructed the first infinite family of v1-periodic elements in his study of the J-homomorphism; showing the nontriviality of these elements requires use of what is known as the e-invariant. A more modern approach to show nontriviality involves the Adams and Adams-Novikov spectral sequences, and an even more modem approach categorifies this into F2-synthetic spectra. This talk will give a brief introduction to v1-periodicity before discussing the Carrick--Davies (arXiv:2401.16508v2) method to detecting v1-periodicity via F2-synthetic spectra.