Book Review: Finiteness theorems for limit cycles

Finiteness Theorems for Submersions and Souls

The first section of this paper provides an improvement upon known finiteness theorems for Riemannian submersions; that is, theorems which conclude that there are only finitely many isomorphism types of fiber bundles among Riemannian submersions whose total spaces and base spaces both satisfy certain geometric bounds. The second section of this paper provides a sharpening of some recent theorem...

Some Finiteness Theorems for Abelian Varieties

Last time we saw (see Proposition 6.5 in those lecture notes) that an abelian variety A of dimension g over K, the fraction field of a henselian dvr R, acquires semistable reduction over K(A[`]) for ` equal to 4 or an odd prime, with ` not divisible by the residue characteristic. (The same circle of ideas yielded the non-obvious fact that over K the intersection of two “semistable field extensi...

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.

Limit Theorems for Bivariate Appell

Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...

Local Limit Theorems for Free