Abstract We study monotone and strictly Hurwitz numbers from a bosonic Fock space perspective. This yields to an interpretation in terms of tropical geometry involving local multiplicities given by Gromov-Witten invariants. Furthermore, this enables us prove that main result Cavalieri-Johnson-Markwig-Ranganathan is actually equivalent the Gromov-Witten/Hurwitz correspondence Okounkov-Pandharipa...

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the pr...

The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these ...

A complete description of the Alexander modules of knotted n-manifolds in the sphere S n+2 , n ≥ 2, and irreducible Hurwitz curves is given. This description is applied to investigate properties of the first homology groups of cyclic coverings of the sphere S n+2 and the projective complex plane CP 2 branched respectively alone knotted n-manifolds and along irreducible Hurwitz (in particular, a...

We present a new realizable reduced order modeling technique for RLC interconnect trees. Both lumped and distributed wire models can be used with this technique. Provable stability is achieved by using Hurwitz polynomials. Moment computation process is avoided but moments can still be matched implicitly. In experiments, the proposed Hurwitz three-pole model can accurately and efficiently captur...

Abstract. We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mariño and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with ChiuChu Melissa Liu and Kefeng Liu. We also compare with some related results on Hurwitz numbers and obtain some closed expressions for the generating series of Hurwitz nu...