Doosung Park - Triangulated categories of logarithmic motives over a field

There are many non A¹-invariant cohomology theories like Hodge cohomology theories. To incorporate these in the framework of triangulated categories of motives, we can instead use a compactification of A¹ in logarithmic geometry, which we call Cube. One technical problem is that Cube does not admit a multiplication map, so Cube is not an interval object in the sense of Morel and Voevodsky. In particular, the naive Sing functor is not useful. In this talk, I will explain how to construct a Sing functor for Cube that can be used to compare Voevodsky's motives and logarithmic motives.