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：A note of Hochmam: the dimension of projections and Furstenberg's dimensional

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： A note of Hochmam: the dimension of projections and Furstenberg's dimensional

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：In this talk, we introduce a recent work of Hochman on the dimension of projections. Let $a,b/ge 2$ be two integers with $/log a//logb/not{in} Q$. 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 by Furstenberg 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 $/dim X+/dim Y<1/2$, the aboveconjecture is valid.In Hochmam's argument, a notion called {/em CP-chain} plays anessential role. Moreover, it has been proved that such a notion is also very useful to attack other problems in geometric measure theory. So, in the first part, we focus on basic properties of CP-chain. In the second part, we will see how the conjecture is linked with CP-chain and also Hochman's proof will be illustrated.