Defeat of the ${\rm FP}\sp 2{\rm F}$ conjecture: Huckaba’s example

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A counter-example to the Cantelli conjecture

In this paper, we construct a counter-example to a question by Cantelli, asking whether there exists a non-constant positive measurable function φ such that for i.i.d. r.v. X,Y of law N (0, 1), the r.v. X + φ(X) · Y is also Gaussian. For the construction that we propose, we introduce a new tool, the Brownian mass transport: the mass is transported by Brownian particles that are stopped in a spe...

Serre's Conjecture over F 9

In this paper we show that an odd Galois representation ¯ ρ : Gal(¯ Q/Q) → GL 2 (F 9) satisfying certain local conditions at 3 and 5 is modular. Our main tool is an idea of Taylor [12], which reduces the problem to that of exhibiting points on a Hilbert modular surface which are defined over a solvable extension of Q, and which satisfy certain reduction properties. As a corollary, we show that ...

A counter-example to the Andreotti-Grauert conjecture

Let X be an analytic complex space which is q-complete. Then it follows from a theorem of Andreotti-Grauert [1] that H(X,F) = 0 for every coherent analytic sheaf F on X if p ≥ q. Until now it is not known if these two conditions are equivalent. The aim of this article is to give a counterexample to the converse of this statement. We show that there exist for each n ≥ 3 open sets Ω ⊂ I C such th...

On the Midpath Tree Conjecture A Counter Example

Introduction Clustering data based on pairwise distances is a fundamental problem Weighted trees can be used to represent hierarchical clusters Multidi mensional Scaling MDS in some formulations is the problem of clustering data based on preserving their relative rather than absolute distances We call this an ordinal clustering A particular instance of this problem has been con sidered in the a...