**Title:** Trace methods in Real algebraic K-theory

**Speaker:** Emanuele Dotto

**Speaker Info:** MIT

**Abstract:**

The Hermitian K-theory of a ring with an antistructure is a topological group completion for the monoid of Hermitian forms on the ring. Recent work of Hesselholt and Madsen describes Hermitian K-theory as the fixed points of a genuine Z/2-spectrum: the Real K-theory spectrum of the ring. Their construction uses a variant of Waldhausen's Sdot construction on categories with duality. This categorical approach makes it possible to construct trace maps to Real variants of THH an TC, as maps of Z/2-spectra. The talk will focus on how, via the trace map, "the equivariant Goodwillie derivative of Real K-theory is Real THH".

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