Related papers: Two-stage spaces and the torus rank conjecture

The paper presents a new short proof of one of Adams's theorems and a $t$-trace-class theorem for parabolic Morrey spaces.

We describe Taylor towers for spaces of knots arising from Goodwillie-Weiss calculus of the embedding functor and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We show that…

We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local…

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

We prove a conjecture stated in a previous paper by the author about the existence of canonical filtrations for a family of vertex operator algebras in rational levels.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We prove the 2-torus $\mathbb T$, an abelian linear algebraic group, is a fine moduli space of labeled, oriented, possibly-degenerate inscribable similarity classes of triangles, where a triangle is {\it inscribable} if it can be inscribed…

This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We study the Picard rank of smooth toric Fano varieties possessing families of minimal rational curves of given degree. We discuss variants of a conjecture of Chen-Fu-Hwang and prove a version of their statement that recovers the original…

A new codimension 2 relation among descendent strata in the moduli space of stable, 3-pointed, genus 2 curves is found. The space of pointed admissible double covers is used in the calculation. The resulting differential equations satisfied…

Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming…

This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve with a single point of order two that does not have a cyclic 4-isogeny defined over its two-division field. We…

We describe some open questions related to support points in the class $S^0$ and introduce some useful techniques toward a higher dimensional Bieberbach conjecture.

In this paper, we construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conjecture.

We show that in codimension at least 3, spaces of locally flat topological embeddings of manifolds are correctly modelled by derived spaces of maps between their configuration categories (under mild smoothability conditions). That general…

We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative…

The volume conjecture, formulated recently by H. Murakami and J. Murakami, is proved for the case of torus knots.

Hartshorne's conjecture about vector bundles on projective space states that any rank 2 vector bundle on n-dimensional projective space splits as soon as n is at least 7. Klyachko has shown that Hartshorne's conjecture is true when the…

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.