Related papers: The Kashiwara-Vergne conjecture

Recently, F. Brenti put a preprint on the arXiv with several interesting open problems on Coxeter groups and unimodality. In this note, we refute one of these conjectures with a counterexample and provide supporting data related to it. This…

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.

The purpose of this paper is to make an introduction to univalent function theory for readers of any level, assuming only foundational knowledge in real and complex analysis. In particular, we state and proof (with details) important…

We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this…

We prove a conjecture of Sturmfels, Timme and Zwiernik on the ML-degrees of linear covariance models in algebraic statistics. As in our previous works on linear concentration models, the proof ultimately relies on the computation of certain…

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…

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

Let Q be an affine quiver and let $\mathfrak{n}$ be the positive part of the affine Lie algebra associated to Q. We provide a construction of $\mathfrak{n}$ using the semistable irreducible components in the Lusztig nilpotent variety…

We formulate a new equivariant Main Conjecture in Iwasawa theory of number fields and study its properties. This is done for arbitrary one-dimensional $p$-adic Lie extensions $L_\infty/K$ containing the cyclotomic $\mathbb{Z}_p$-extension…

It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules associated to a finite Coxeter group are related by the…

We solve a generalised form of a conjecture of Kalai motivated by attempts to improve the bounds for Borsuk's problem. The conjecture can be roughly understood as asking for an analogue of the Frankl-R\"odl forbidden intersection theorem in…

We prove a conjecture of Kashiwara and Miemietz on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case.

Assuming that Iwasawa's $\mu_{K/k}$-invariant vanishes, we prove the 'main conjecture' of equivariant Iwasawa theory, at odd prime numbers $l$, for arbitrary extensions $K/k$ of totally real number fields, up to its uniqueness assertion.

We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.

In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…

We derive some combinatorial consequences from the positivity of Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for…

In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.

The Caccetta-Haggkvist conjecture states that if G is a finite directed graph with at least n/k edges going out of each vertex, then G contains a directed cycle of length at most k. Hamidoune used methods and results from additive number…

The Kashiwara-Vergne Lie algebra $\mathfrak{krv}$ encodes symmetries of the Kashiwara-Vergne problem on the properties of the Campbell-Hausdorff series. It is conjectures that $\mathfrak{krv} \cong \mathbb{K}t \oplus \mathfrak{grt}_1$,…

We prove Union-Closed sets conjecture.