In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler’s equation) of the Hurwitz Frobenius manifolds. Second, in terms of this tau-function we compute the genus one correction to the free energy ...

We extend results of Borcea and Brändén to quantitatively bound the movement of the zeros of Hurwitz stable polynomials under linear multiplier operators. For a multiplier operator T on polynomials of degree up to n, we show that the ratio between the maximal real part of the zeros of a Hurwitz stable polynomial f and that of its transform T [f ] is minimized for the polynomial (z + 1). For T o...

In this paper, we investigate the disturbance attenuation properties of timecontrolled switched systems consisting of several linear time-invariant subsystems by using a dwell time approach incorporated with piecewise Lyapunov functions. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than γ0, then the switched system can achieve an...

In this research-cum-expository article, we aim at presenting a systematic account of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a) as well as its various interesting extensions and generalizations. In particular, we begin by looking into the problems associated with the evalu...

We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of P with given ramification over ∞ and sufficiently many fixed ramification points elsewhere. Degeneration of the target and judicious localization expresses such classes in terms of localization trees weighted by “top intersections” of tautologi...

This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov-Witten theory, with a particular eye to the contributions made to the understanding of the Double Ramification Cycle, a cycle in the moduli space of curves that compactifies the double Hurwit...

The Hurwitz space is a compactification of the space of rational functions of a given degree. The Lyashko–Looijenga map assigns to a rational function the set of its critical values. It is known that the number of ramified coverings of CP by CP with prescribed ramification points and ramification types is related to the degree of the Lyashko–Looijenga map on various strata of the Hurwitz space....