Related papers: Automorphy lifting for small l

We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.

We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…

The objective of this paper is the proof of a conjecture of Kontsevich on the isomorphism between groups of polynomial symplectomorphisms and automorphisms of the corresponding Weyl algebra in characteristic zero. The proof is based on the…

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the L\"uck Approximation Theorem…

We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…

We show that Alexander's extendibility theorem for a local automorphism of the unit ball is valid also for a local automorphism $f$ of a pseudoellipsoid $\E^n_{(p_1, ..., p_{k})} \= \{z \in \C^n : \sum_{j= 1}^{n - k}|z_j|^2 + |z_{n-k+1}|^{2…

We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$…

We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n \geq 4$. For minimizing harmonic maps $u\in W^{1,2}(\Omega,\mathbb{S}^2)$ from $n$-dimensional domains into the two dimensional sphere we prove: (1)…

This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…

In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…

In this short note, we given a new proof of Mitchell's theorem that $L_{T\left(n\right)} K(Z) \cong 0$ for $n \geq 2$. Instead of reducing the problem to delicate representation theory, we use recently established hyperdescent technology…

We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, that have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions…

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…

A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…

We study the automorphisms of compact K\"ahler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that…

Let $\mathcal{F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb{R}$ such that $\int f = 1$. We determine the value of $\inf_{f \in \mathcal{F}} \| f \ast f \|_2$ up to a 0.0014\% error, thereby making progress on a problem…

We explore the lifting question in the context of cut-generating functions. Most of the prior literature on this question focuses on cut-generating functions that have the unique lifting property. We develop a general theory for…

The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation…

It is well known that every locally compact abelian group L can be decomposed as L_1 \oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of…

An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…