# Özgür Bayındır: Postdoc day, Seminar 1: Adjoining roots to ring spectra and algebraic K-theory

**Time: **
Fri 2022-02-18 13.30 - 14.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Lecturer: **
Özgür Bayındır (University Paris 13)

**Abstract:** In this work, we start with a new method to adjoin roots to \(E_2\) ring spectra. We prove that this process is logarithmic THH étale and that it results in interesting splittings in algebraic K-theory. For instance, we obtain that \(T(n+1)\)-locally, the algebraic K-theory of the nth Morava E-theory contains the algebraic K-theory of the truncated Brown-Peterson spectrum with coefficients as a summand. In particular, this provides a proof of the fact that Morava E-theories satisfy the redshift conjecture. This is a joint work with Tasos Moulinos and Christian Ausoni.