Title: On the structure of translational tilings

Abstract: Let F be a finite subset of a finitely generated abelian group G. We say that F is a translational tile of G, if G can be partitioned into translated copies of F. The well-known periodic tiling conjecture asserts that any translational tile admits at least one periodic tiling. In the talk, we will motivate and discuss the study of this conjecture as well as its connections to other questions. We will also present some recent results, joint with Terence Tao, on the structure of translational tilings in finitely generated abelian groups, and suggest some open problems.

About the Speaker: Rachel Greenfeld got her  PhD at the Mathematics Department of Bar Ilan University in 2019 under the direction of Nir Lev.  She is currently a Hedrick Assistant Adjunct Professor in the Department of Mathematics at UCLA, fortunate to work with Terence Tao. Dr. Greenfeld is particularly interested in harmonic analysis and its applications and connections to related areas such as combinatorics, number theory, ergodic theory and geometric measure theory.