## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Algebraically closed fields in higher algebra

**Speaker:** Allen Yuan

**Speaker Info:** Columbia University

**Brief Description:**

**Special Note**:

**Abstract:**

Higher algebra is a homotopical enlargement of algebra where algebraic structures, such as rings and modules, have underlying spaces as opposed to just underlying sets. A striking feature of higher algebra is that there are additional "chromatic characteristics" interpolating between characteristic 0 and characteristic p. These intermediate characteristics have shed light on mod p phenomena in geometry, number theory, and representation theory. At the same time, the extension of algebraic ideas to higher algebra has been fruitful within algebraic topology: I will discuss joint work with Robert Burklund and Tomer Schlank which proves a higher analogue of Hilbertâ€™s Nullstellensatz, thus identifying the algebraically closed fields of intermediate characteristic. In addition to initiating the study of "chromatic algebraic geometry," this work resolves a form of Rognesâ€™ chromatic redshift conjecture in algebraic K-theory.

**Date:** Monday, November 28, 2022

**Time:** 4:00pm

**Where:** Lunt 105

**Contact Person:** Benjamin Antieau

**Contact email:** antieau@northwestern.edu

**Contact Phone:** 847-491-5544

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Department of Mathematics, Northwestern University.