Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized non-escaping critical points, generalizing a result of Douady-Hubbard for quadratic polynomials to the case higher degree polynomials. This solves affirmatively conjecture by Inou and Kiwi on surjectivity renormalization operator in one complex variab...

For a random matrix of entries sampled independently from fairly general distribution in $${{\mathbf {Z}}}$$ we study the probability that cokernel is isomorphic to given finite abelian group, or when it cyclic. This includes linear map between integer lattices by surjective. We show these statistics are asymptotically universal (as size goes infinity), precise formulas involving zeta values, a...

Free Data Structures are finite semantic trees modulo equational axioms that are useful to represent classical data structures such as lists, multisets and sets. We study the satisfiability problem when free data structures are combined with bridging functions. We discuss the possibility to get a combination method à la Nelson-Oppen for these particular non-disjoint unions of theories. In order...

We prove surjectivity of the comparison map from continuous bounded cohomology to continuous cohomology for Hermitian Lie groups with finite center. For general semisimple Lie groups with finite center, the same argument shows that the image of the comparison map contains all the even degree primitive elements. Our proof uses a Hirzebruch type proportionality principle in combination with Gromo...