Related papers: Shokurov's index conjecture for quotient singulari…

We prove several congruences for trinomial coefficients.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

The purpose of this paper is to lay the foundations for the theory of higher rank b-divisorial algebras of Shokurov type. We develop techniques to deal with such objects and propose two natural conjectures regarding Shokurov algebras and…

We give a simple way to extend index-theoretical statements from partial differential operators with smooth coefficients to operators with coefficients of finite Sobolev order.

Let $S=(a_1)\cdots(a_k)$ be a minimal zero-sum sequence over a finite cyclic group $G$. The index conjecture states that if $k=4$ and $\gcd(|G|,6)=1$, then $S$ has index $1$. In this paper we prove that if $S$ is singular then the index of…

We prove Fujita's spectrum conjecture on the discreteness of pseudo-effective thresholds for polarized varieties.

We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.

We define for families of finite metric spaces quantitative assembly map estimates that take into account propagation phenomena for pseudo-differential calculus. We relate these estimates to the Novikov conjecture and we show that they fit…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We prove the precise inversion of adjunction formula for quotient singularities. As an application, we prove the semi-continuity of minimal log discrepancies for hyperquotient singularities. This paper is a continuation of arXiv:2011.07300,…

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.

We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov's conjecture is true for log-terminal threefolds.

We prove a curious identity for the Bernoulli numbers.

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.

Herzog and Sch\"onheim conjectured that any nontrivial partition of a group into cosets must contain two cosets with the same index.

We prove the even isomorphism theorem for Coxeter groups

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

A simple proof of Egorov's theorem for infinite measure is given

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.