相关论文: A correction to: Rational and nearly rational vari…
The hyperbolicity statements for subvarieties and complements of hypersurfaces in abelian varieties admit arithmetic analogues, due to Faltings (and Vojta for the semi-abelian case). In Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29…
Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U.…
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
This note complements our paper "Categoricity-like properties in the first order realm" (Journal for the Philosophy of Mathematics, 2024).
Significant controversy remains about what constitute correct self-locating beliefs in scenarios such as the Sleeping Beauty problem, with proponents on both the "halfer" and "thirder" sides. To attempt to settle the issue, one natural…
For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd…
We correct an error in the article "Property (RD) for Hecke pairs".
Let $X$ be a smooth projective split horospherical variety over a number field $k$ and $x\in X(k)$. Contingent on Vojta's conjecture, we construct a curve $C$ through $x$ such that (in a precise sense) rational points on $C$ approximate $x$…
We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.
We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the…
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
Given a flag variety $X$ defined over $\mathbb{Q}$ and a point $x$ in $X(\mathbb{R})$, we study approximations to $x$ by points $v$ in $X(\mathbb{Q})$, and show that, with an appropriate rescaling, those approximations equidistribute when…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
This paper corrects some mathematical errors in Holmstr\"om (1999) and clarifies the assumptions that are sufficient for the results of Holmstr\"om (1999). The results remain qualitatively the same.
We study truthful mechanisms for approximating the Maximin-Share (MMS) allocation of agents with additive valuations for indivisible goods. Algorithmically, constant factor approximations exist for the problem for any number of agents. When…
Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…
We prove two correlation inequalities .
We prove that every proper subclass of the 321-avoiding permutations that is defined either by only finitely many additional restrictions or is well quasi-ordered has a rational generating function. To do so we show that any such class is…
The proofs of Theorem 3.1 and Corollary 4.1 in Le\~ao and Ohashi (2013) are incomplete. The reason is a wrong statement in Remark 2.2. The hypotheses and statements of Theorem 3.1 and Corollary 4.1 in Le\~ao and Ohashi (2013) remain…
This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.