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We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Marde\v{s}i\'{c} and Prasolov…
The classical Riemann-Roch theorem has been extended by N. Nadirashvili and then M. Gromov and M. Shubin to computing indices of elliptic operators on compact (as well as non-compact) manifolds, when a divisor mandates a finite number of…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we present a series of time dependent benchmark inverse…
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential…
We study local biholomorphisms with finite orbits in some neighborhood of the origin since they are intimately related to holomorphic foliations with closed leaves. We describe the structure of the set of periodic points in dimension 2. As…
It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958, Giorgilli 2001). The unstable and stable manifolds…
A long-standing conjecture of Littlewood about simultaneous Diophantine approximation has an analogous problem for a field of formal Laurent series $\mathbb{F}(\!(t^{-1})\!)$. That is, we can ask whether for any series $\Theta$, $\Phi$ and…
In the beginning of the 20th century, A. N. Whitehead and T. de Laguna proposed a new theory of space, known as {\em region-based theory of space}. They did not present their ideas in a detailed mathematical form. In 1997, P. Roeper has…
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…
We investigate the regularity of local weak solutions to evolution equations of the form \[…
100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was stated in full generality later by Osgood (1929): holomorphic functions in a connected…
Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant challenges when applied to non-rectangular domains and in…
In this paper we generalize work of Amice and Lazard from the early (nineteen) sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
In 2005 Kawamura and Rambla, independently, constructed a metric counterexample to Wood's Conjecture from 1982. We exhibit a new nonmetric counterexample of a space $\hat L$, such that $C_0(\hat L,\mathbb{C})$ is almost transitive, and show…
A local convergence result for abstract descent methods is proved. The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges within this neighborhood. This result allows algorithms to…
In this article we study the asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. We present a family of CAT(0) cube complexes on which the latter groups act. Along the way, we…
We give a local treatment of finite alignment by identifying the finitely aligned part of any (not necessarily finitely aligned) higher-rank graph. We show the finitely aligned part is itself a constellation and forms a finitely aligned…
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce…