中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人： 荆一凡  博士（University of Oxford）

题  目：Sets of integers with no solutions to certain linear equations

时  间：2022.04.01（星期五），15:00-17:00

地  点：腾讯会议：905-515-100 密码：123456

摘  要：Given a dilation invarient linear equation L and a set A of N integers, what is the size of the largest subset of A that avoids solutions to L? This problem in additive and combinatorial number theory looks simple, yet the exact bounds for many L remain unsolved even if A is the first N integers. In this talk, we will discuss two classic problems in this direction, the Erdos sum-free conjecture, and the sum-product phenomenon for Sidon sets. This talk is based on some recent joint work with Shukun Wu and with Akshat Mudgal.