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We construct the counter-example for polynomial version of Sarnaks conjecture for minimal systems, which assets that the Mobius function is linearly disjoint from subsequences along polynomials of deterministic sequences realized in minimal systems. Our example is in the class of Toeplitz systems, which are minimal.
In this paper, we provide a counter-example to the ER=EPR conjecture. In an anti-de Sitter space, we construct a pair of maximally entangled but separated black holes. Due to the vacuum decay of the anti-de Sitter background toward a deeper vacuum, t
We demonstrate how recent work of Favre and Gauthier, together with a modification of a result of the author, shows that a family of polynomials with infinitely many post-critically finite specializations cannot have any periodic cycles with multipli
In this paper, we reduce the logarithmic Sarnak conjecture to the ${0,1}$-symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture holds for any topologically dynamical system with sublinear complexity, we p
It is widely believed that anisotropy in the expansion of the universe will decay exponentially fast during inflation. This is often referred to as the cosmic no-hair conjecture. However, we find a counter example to the cosmic no-hair conjecture in
Sarnaks Density Conjecture is an explicit bound on the multiplicities of non-tempered representations in a sequence of cocompact congruence arithmetic lattices in a semisimple Lie group, which is motivated by the work of Sarnak and Xue. The goal of t