Related papers: A short proof of the irreflexivity conjecture
We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by noncommutative Laurent polynomials.
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.
An equivalent but useful version on the Homological Nerve Theorem is proved.
We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this fact using only simple planar topology is presented.
We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by Knuth in [4].
Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism…
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
Given the single-letter capacity formula and the converse proof of a channel without constraints, we provide a simple approach to extend the results for the same channel but with constraints. The resulting capacity formula is the minimum of…
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
In this survey paper we present recent results obtained by Khare, Wintenberger and the author that have led to a proof of Serre's conjecture, such as existence of compatible families, modular upper bounds for universal deformation rings and…
In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and…
We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately…
We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).
We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.