关于举行华中科技大学王保伟教授和徐剑教授学术报告的通知

报告题目1：Anote of Hochmam: the dimension of projections and Furstenberg'sdimensional

conjecture(I)

报告人：王保伟教授（华中科技大学）

报告时间：11月30日（周一）下午15：00--16：00

报告地点：4号楼4141室

报告题目2：Anote of Hochmam: the dimension of projections and Furstenberg'sdimensional

conjecture(II)

报告人：徐剑教授（华中科技大学）

报告时间：11月30日（周一）下午16：15--17：15

报告地点：4号楼4141室

      欢迎广大师生前往!

                                      数学学院

                                   2015年11月26日

报告摘要：Inthis talk, we introduce a recent work of Hochman on the dimension ofprojections. Let $a,b\ge 2$ be two integers with $\loga/\logb\not{in} Q$. Let $X$ be a closed $f_a$-invariant subset in$[0,1]$ and $Y$ a closed $f_b$-invariant subset in $[0,1]$, where$f_a(x)=ax\ ({\text{mod}}\ 1)$.  It was conjectured byFurstenberg among others that for any $v$ and $u\ne 0$, $$\dim\Big((X\times Y)\cap \{(x,y): y=ux+v\}\Big)\le \max\Big\{0,\dimX+\dim Y-1\Big\}.$$ It is proved by Hochman that if $\dim X+\dimY<1/2$, the aboveconjecture is valid.In Hochmam's argument, anotion called {\em CP-chain} plays anessential role. Moreover, it hasbeen proved that such a notion is also very useful to attack otherproblems in geometric measure theory. So, in the first part, we focuson basic properties of CP-chain. In the second part, we will see howthe conjecture is linked with CP-chain and also Hochman's proof willbe illustrated.