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We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses b...
The number of PL-homeomorphism types of combinatorial manifolds in a fixed dimension with an upper bound on g2 is finite.
We prove the niteness of class numbers and Tate-Shafarevich sets for all ane group schemes of nite type over global function elds, as well as the niteness of Tamagawa numbers and Godement's com...
In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree st...
Abstract: In this paper, we prove that every orientable closed 3-manifold dominates at most finitely many homeomorphically distinct irreducible non-geometric 3-manifolds. Moreover, for any integer $d>...
Abstract: Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. In this paper, we study relations between f...
Abstract: We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) a...
Abstract: Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show that the number of gauge groups of principal $G$-bundles over $B$ is finite up to $A_n$-equivalence for $n<\inft...
Abstract: Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only finitely man...
Abstract: Let $\bS=\{S_1,...,S_K\}$ be a finite set of complex $d\times d$ matrices and $\varSigma_{K}^+$ the compact space of all one-sided infinite sequences $i_{\bcdot}\colon\mathbb{N}\rightarrow\{...
We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach for these classes.
Given a graded sequence of ideals (a_m) on a smooth variety X, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log discrepanc...
Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the exist...
We introduce the notion of a Schur-finite element in a $\lambda$-ring.
We show that Brin’s generalisations 2V and 3V of the Thompson-Higman group V are of type FP1. Our methods also give a new proof that both groups are finitely presented.

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