turkmath.org

The category of spectra captures an important part of the complexity of topological spaces while providing generalizations of many important notions in homological algebra. In this work, we develop a new method to adjoin roots to ring spectra and show that this process results in interesting splittings in algebraic $K$-theory. In the first part of my talk, I will provide motivation for algebraic $K$-theory and highly structured ring spectra. After this, I will discuss trace methods, a program that provides computational tools for algebraic $K$-theory, and introduce our results.
This is a joint work in progress with Tasos Moulinos and Christian Ausoni.