Related papers: On a conjecture for Rubin-Stark elements in a spec…

In this survey paper we study Manin's Conjecture from a geometric perspective. The focus of the paper is the recent conjectural description of the exceptional set in Manin's Conjecture due to Lehmann-Sengupta-Tanimoto. After giving an…

We prove the Aharoni Berger Conjecture

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We conjecture that the exceptional set in Manin's Conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically finite map with larger geometric invariants. We prove that this…

Let $N$ and $p$ be prime numbers $\geq 5$ such that $p$ divides $N-1$. Let $I$ be Mazur's Eisenstein ideal of level $N$ and $H_+$ be the plus part of $H_1(X_0(N), \mathbf{Z}_p)$ for the complex conjugation. We give a conjectural explicit…

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.

The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.

Let $k$ be an imaginary quadratic number field, and $F/k$ a finite abelian extension of Galois group $G$. We investigate the relationship between the conjectural special elements introduced in \cite{Burns-DeJeu-Gangl} and ETNC in the…

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

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

This paper presents our proof of the "strong Macdonald constant term conjecture" of P. Hanlon and B. Feigin.

We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).

We introduce an integral version of the Eisenstein cocycle. As applications we prove a conjecture of Gross regarding the "order of vanishing" of Stickelberger elements relative to an abelian tower of fields and give a cohomological…

In this talk we discuss possible signatures for the existence of strange quark matter stars (strange stars).

This paper improves some results of the author's previous work. We will investigate the case of non-smooth points on an automorphic components and prove Breuil-Schenider conjecture. As a consequence we will see that in case when all the…

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…

We introduce the notion of Shintani data, which axiomatizes algebraic aspects of Shintani zeta functions. We develop the general theory of Shintani data, and show that the order of vanishing part of Gross's conjecture follows from the…

Given an abelian, CM extension K of any totally real number field k, we consider two conjectures `of Stark type'. The `Integrality Conjecture' concerns the image of a p-adic map `\mathfrak{s}_{K/k,S}' determined by the minus-part of the…