Related papers: Sticky matroids and Kantor's Conjecture
The volume conjecture, formulated recently by H. Murakami and J. Murakami, is proved for the case of torus knots.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
Samuel J. Lomonaco Jr and Louis H. Kauffman conjectured that tame knot theory and knot mosaic theory are equivalent. We give a proof of the Lomonaco-Kauffman conjecture.
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
Gao and Xie (2021) conjectured that the inverse Kazhdan-Lusztig polynomial of any matroid is log-concave. Although the inverse Kazhdan-Lusztig polynomial may not always have only real roots, we conjecture that the Hadamard product of an…
This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.
We introduce a ``hybrid'' conjecture which is a common generalisation of the Andr\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture and we prove that it is a consequence of the Zilber-Pink conjecture. We also show that our hybrid…
We prove a conjecture about the concordance invariant $\vartheta$, defined in a recent paper by Lewark and Zibrowius. This result simplifies the relation between $\vartheta$ and Rasmussen's $s$-invariant. The proof relies on Bar-Natan's…
Let $M$ be a matroid without loops or coloops and let $T(M;x,y)$ be its Tutte polynomial. In 1999 Merino and Welsh conjectured that $$\max(T(M;2,0), T(M;0,2))\geq T(M;1,1)$$ holds for graphic matroids. Ten years later, Conde and Merino…
We settle three problems from the literature on stable and real zero polynomials and their connection to matroid theory. We disprove the weak real zero amalgamation conjecture by Schweighofer and the second author. We disprove a conjecture…
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective extends ideas of Beilinson and Bondal to all semiprojective…
It is conjectured that for every convex disks K, the translative covering density of K and the lattice covering density of K are identical. It is well known that this conjecture is true for every centrally symmetric convex disks. For the…
In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…
In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
In this paper, we prove Gromov's flat corner domination conjecture in all dimensions. As a consequence, we answer positively the Stoker conjecture for convex Euclidean polyhedra in all dimensions. By applying the same techniques, we also…