Title: Non-sliceness of cables of figure-eight knot via real Seiberg-Witten theory

Abstract: Cables of the figure-eight knot are related to the slice-ribbon conjecture: if any of them are smoothly slice, then the slice-ribbon conjecture is false. In a work of Dai-K.-Mallick-Park-Stoffregen, the case of a (2,1)-cable was proven to be non-slice, which was generalized to non-sliceness of (4n+2,1)-cables in a work of K.-Park-Taniguchi. In this talk, we show that all cables of the figure-eight knot are not smoothly slice, and furthermore, they have infinite order in the smooth knot concordance group, using various tools in real Seiberg-Witten theory. This is a joint work with JungHwan Park and Masaki Taniguchi.