报告时间:2023111016:00-16:50

报告地点:天赐庄校区维格堂319

报告人:吴健超研究员(上海数学中心)

报告题目:Long thin covers and nuclear dimension of C*-algebras  

报告摘要:

A recurring theme in the study of C*-algebras is their strong ties to topological dynamical systems, paralleling the fruitful interplay between von Neumann algebra theory and ergodic theory. The breakthroughs in the Elliott classification program of C*-algebras in the last decade have led to a prominent question around this theme, namely: when does the C*-algebra arising from a topological dynamical system satisfy finite nuclear dimension?

In a recent preprint (joint with Hirshberg), we verify finite nuclear dimension for any (crossed product) C*-algebra arising from an action by a finitely generated virtually nilpotent group on a finite-dimensional space. This is shown by introducing a new topological-dynamical dimension concept called the long thin covering dimension. This result can be strengthened further and applied to some allosteric (and thus non-almost-finite) actions by certain wreath product groups. Another application yields the result (joint with Eckhardt) that (twisted) group C*-algebras of virtually polycyclic groups have finite nuclear dimension.

报告人简介:

吴健超,复旦大学上海数学中心青年研究员,博士毕业于美国范德堡大学,入选国家级青年人才计划,研究领域为非交换几何和算子代数。在Geom. Funct. Anal.Adv. Math.Comm. Math. Phys.Trans. Amer. Math. Soc.等知名数学期刊发表多篇论文。

邀请人:梁兵兵 教授