题目：A Kaufman type restricted projection theorem to lines in $\mathbb R^3$

时间：北京时间2023年5月26日（周五）上午10：00

地点：鼓楼校区西大楼108报告厅

腾讯会议   ID：860-849-669  密码：230526

报告人：杨童鸥  Tongou Yang, University of Wisconsin-Madison

摘要：Given a $C^2$ nondegenerate curve lying on the unit sphere in three dimensions. We answer a question of Fässler and Orponen, which says that for any Borel set $A$, its projection into almost all directions determined by the image of the curve

has a sharp Hausdorff dimension given by $\min\{\mathrm{dim}(A),1\}$. We achieve this by proving a Kaufman type estimate on the Hausdorff dimension of the exceptional set. One key feature of our argument is a result of Marcus-Tardos in topological graph theory, and our proof does not use any Fourier analysis. We also point out other recent developments of this problem. This is joint work with Malabika Pramanik and Joshua Zahl.