Tom Bachmann - The Chow t-structure for motivic spectra (Joint with Kong, Wang, Zhu)
The category of motivic spectra over a field admits a t-structure, with non-negative part generated by the Thom spectra of virtual vector bundles on smooth proper varieties. This is called the Chow t-structure. Perhaps its most surprising property is the close connection to algebraic cobordism. I will explain this, as well as how the Chow t-structure recovers and generalizes the celebrated "cofiber tau" theory of Isaksen-Gheorghe et al.