Related papers: Shokurov's index conjecture for quotient singulari…
We prove some symmetric $q$-congruences.
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
Results in the preliminary version have been strengthed. In addition, Batyrev's conjectural formula for quantum cohomology of projective bundles associated to direct sum of line bundles over $\Pee^n$ is partially verified.
We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.
We extend the holographic formula for the critical $Q$-curvature to all $Q$-curvatures.
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
We proved that there are infinitely many cousin primes.
We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially from the commutative case.
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
For a birational analogue of minimal elliptic surfaces X/Y, the singularities of the fibers define a log structure in codimension one on Y. Via base change, we have a log structure in codimension one on Y', for any birational model Y' of Y.…
We present a proof of a conjecture proposed by T. Yano about the generic $b$-exponents of irreducible plane curve singularities.
We prove universality for cokernels of random integral matrices with symmetries via an approach different from the classical surjection moment method introduced by Wood (arXiv:1402.5149). In the symmetric case, we reprove Hodges'…
We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$…
A problem in zero-sum theory is to determine all pairs $(k,n)$ for which every minimal zero-sum sequence of length $k$ modulo $n$ has index $1$. While all other cases have been solved more than a decade ago, the case when $k$ equals $4$ and…
We establish a Bombieri-Vinogradov theorem for sectors in real quadratic number fields.
We prove that the quotient of the integer homology cobordism group by the subgroup generated by the Seifert fibered spaces is infinitely generated.
In this note, we prove the magnetic spectral gap-labelling conjecture as stated in [arXiv:1508.01064], in all dimensions, for principal solenoidal tori.
We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…