Tensor-triangular geometry is the study of stable \(\infty\)-categories equipped with multiplicative structures through a geometric lens. Of particular interest is the study of the Balmer spectrum, which contains a lot of information about the structure of such an object. I follow closely the developments of the subject, and often think about it.
My main contribution here is with Tobias Barthel and Logan Hyslop : we prove that Balmer's "Nerves of Steel conjecture" is false in general (though Logan has some interesting results which establish it in some generality, see his website for more). This result of ours suggests looking at more free examples in tensor-triangular geometry, and that the "geometric" examples classically studied were, well, too geometric to reveal the failure of this conjecture.