中科院数学与系统科学研究院

数学研究所

学术报告

数理逻辑研讨班

报告人：Isaac Goldbring（University of California）   

题  目：Preliminary remarks on the first-order free group factor problem

时  间：2022.01.13（星期五）上午10:00-12:00

地  点：腾讯会议: 311-0934-3182

摘  要：A standard construction in von Neumann algebra theory is to construct the group von Neumann algebra L(G) associated to any discrete group G.  This process can “forget” much of the algebraic information about the group.  For example, a celebrated result of Connes implies that any two discrete amenable groups all of whose nontrivial conjugacy classes are infinite yield the same von Neumann algebra.  A famous open question in the subject is whether or not L(F_m) and L(F_n) are isomorphic for distinct m and n, where F_m denotes the nonabelian free group on m generators.  In this talk, we will discuss some preliminary observations about the model-theoretic version of this question, which asks whether or not L(F_m) and L(F_n) are elementarily equivalent for distinct m and n (which can be viewed as a noncommutative version of the famous Tarski problem, which asks whether or not F_m and F_n are elementarily equivalent and for which the problem is now known to have a positive solution).  The work presented in this talk is joint with Jennifer Pi.  We will assume no prior knowledge of von Neumann algebra theory.

个人网页：https://www.math.uci.edu/~isaac/