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The work of Mike Hochman on multidimensional symbolic dynamics and Borel dynamics
From invariance to selfsimilarity: The work of Michael Hochman on fractal dimension and its aftermath
Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel 
M. Hochman's work on the dimension of selfsimilar sets has given impetus to resolving other questions regarding fractal dimension. We describe Hochman's approach and its influence on the subsequent resolution by P. Shmerkin of the conjecture on the dimension of the intersection of $ \times p $ and $ \times q $Cantor sets.
References:
[1] 
H. Furstenberg, Intersections of Cantor sets and transversality of semigroups. In Problems in Analysis (Symposium in honor of Salomon Bochner, Princeton University Press, Princeton, N.J. 1969), 41–59, 1970. Google Scholar 
[2] 
H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory, 1 (1967), 149. doi: 10.1007/BF01692494. Google Scholar 
[3] 
M. Hochman, On selfsimilar sets with overlaps and inverse theorems for entropy, Ann. of Math. (2), 180 (2014), 773822. doi: 10.4007/annals.2014.180.2.7. Google Scholar 
[4] 
P. Shmerkin, On Furstenberg's intersection conjecture, selfsimilar measures, and the $L^q$norms of convolutions, Ann. of Math. (2), 189 (2019), 319–391. doi: 10.4007/annals.2019.189.2.1. Google Scholar 
[5] 
M. Wu, A proof of Furstenberg's conjecture on the intersection of $\times p$ and $\times q$invariant sets, arXiv: 1609.08053v3, February 2019. Google Scholar 
show all references
References:
[1] 
H. Furstenberg, Intersections of Cantor sets and transversality of semigroups. In Problems in Analysis (Symposium in honor of Salomon Bochner, Princeton University Press, Princeton, N.J. 1969), 41–59, 1970. Google Scholar 
[2] 
H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory, 1 (1967), 149. doi: 10.1007/BF01692494. Google Scholar 
[3] 
M. Hochman, On selfsimilar sets with overlaps and inverse theorems for entropy, Ann. of Math. (2), 180 (2014), 773822. doi: 10.4007/annals.2014.180.2.7. Google Scholar 
[4] 
P. Shmerkin, On Furstenberg's intersection conjecture, selfsimilar measures, and the $L^q$norms of convolutions, Ann. of Math. (2), 189 (2019), 319–391. doi: 10.4007/annals.2019.189.2.1. Google Scholar 
[5] 
M. Wu, A proof of Furstenberg's conjecture on the intersection of $\times p$ and $\times q$invariant sets, arXiv: 1609.08053v3, February 2019. Google Scholar 
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