Related papers: The Deligne-Simpson problem for zero index of rigi…

In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider…

This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive…

Let $X$ be a scheme of finite type over $\mathbf{Z}$. For $p \in \mathcal{P}$ the set of prime numbers, let $N_{X}(p)$ be the number of $\mathbf{F}_{p}$-points of $X/\mathbf{F}_{p}$. For fixed $n\geq 1$ and $a_{1}, \ldots, a_{n} \in…

In this paper, we prove that there exists a universal constant $C$, depending only on positive integers $n\geq 3$ and $p\leq n-1$, such that if $M^n$ is a compact free boundary submanifold of dimension $n$ immersed in the Euclidean unit…

It is commonly accepted that general relativity is the only solution to the consistency problem that appears when trying to build a theory of interacting gravitons (massless spin-2 particles). Padmanabhan's 2008 thought-provoking analysis…

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic 1-form…

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may…

Let $A=(a_{ij})_{n\times n}$ be a nonnegative, symmetric, irreducible and invertible matrix. We prove the existence and uniqueness of radial solutions to the following Liouville system with singularity: $$\{{array}{ll} \Delta…

Motivated by our results in "Polish Models and Sofic Entropy," we define modified version of the independence tuples for sofic entropy developed by Kerr and Li. These modified version essentially require that the independence sequences give…

In this paper, we study combinatorics of congruence subgroups of the modular group. More precisely, we consider the matrix equation that naturally arises in the theory of Coxeter friezes and investigate its irreducible solutions. We give…

Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…

We study the multiplication operation of square matrices over lattices. If the underlying lattice is distributive, then matrices form a semigroup; we investigate idempotent and nilpotent elements and the maximal subgroups of this matrix…

Let N be a square-free positive integer and let f be a newform of weight 2 on \Gamma_0(N). Let A denote the abelian subvariety of J_0(N) associated to f and let m be a maximal ideal of the Hecke algebra T that contains Ann_T(f) and has…

We provide a new large class of countable icc groups $\mathcal A$ for which the product rigidity result from [CdSS15] holds: if $\Gamma_1,\dots,\Gamma_n\in\mathcal A$ and $\Lambda$ is any group such that…

Suppose that for some unit vectors $b_1,\ldots b_n$ in $\mathbb C^d$ we have that for any $j\neq k$ $b_j$ is either orthogonal to $b_k$ or $|\langle b_j,b_k\rangle|^2 = 1/d$ (i.e. $b_j$ and $b_k$ are unbiased). We prove that if $n=d(d+1)$,…

We introduce middle convolution for systems of linear differential equations with irregular singular points, and we presend a tentative definition of the index of rigidity for them. Under some assumption, we show a list of terminal patterns…

We are interested in identities between Littlewood-Richardson coefficients, and hence in comparing different tensor product decompositions of the irreducible modules of the linear group GL n (C). A family of partitions-called…

Let $X$ be a negatively curved symmetric space and $\Gamma$ a non-cocompact lattice in $\rm{Isom}(X)$. We show that small, parabolic-preserving deformations of $\Gamma$ into the isometry group of any negatively curved symmetric space…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

We prove the existence of positive solutions for a class of semipositone problem with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.