报告时间：2025年09月23日 （周二）下午14:30-15:30
报告地点：国交2号楼315会议室
报告人：Gergely Kiss 教授 Budapest Corvinus University and Rényi Institute
摘要：The concept of weak tiling was originally introduced in R^n by Lev and Matolcsi, and has proven to be an essential tool in addressing Fuglede's conjecture for convex domains. In this talk, we extend the notion of weak tiling to the setting of cyclic groups and further generalize it using a natural averaging process. As a result, the tiles are no longer sets, but rather become step functions--a framework we refer to as functional tiling.
One advantage of this approach is that the cyclotomic divisors of the functions involved in a functional tiling remain the same as those of the characteristic functions of the original sets. Another is that functional tilings can be studied using the well-established tools and objective functions of linear programming, which is computationally efficient due to its polynomial-time solvability.
I will introduce the key quantities involved and present basic connections between functional and classical tilings. I will provide a counterexample to the Coven-Meyerowitz conjecture within the context of functional tilings. It is important to note, however, that none of the counterexamples we constructed in this setting correspond to tiling pairs of sets. Thus, the Coven-Meyerowitz conjecture for tiling sets remains open.
This is joint work with Itay Londner, Máté Matolcsi, and Gábor Somlai.
