EVENT DETAILS AND ABSTRACT

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 Hilbert’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 Rognes’ chromatic redshift conjecture in algebraic K-theory.