Related papers: Normal integral bases and Gaussian periods in the …

We construct a twin correspondence between graphs with prescribed mean curvature in three-dimensional Riemannian Killing submersions and spacelike graphs with prescribed mean curvature in three-dimensional Lorentzian Killing submersions.…

For each positive integer $n$, we give a geometric description of the stably trivial elements of the group $\pi_n U_n/O_n$. In particular, we show that all such elements admit representatives whose tangencies with respect to a fixed…

Let $N/F$ be an odd degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak O}_N$ and ${\mathfrak O}_F=\bo$ respectively. Let $\mathcal{A}$ be the unique fractional ${\mathfrak O}_N$-ideal with…

We construct a family of $GL_n$ rational and trigonometric Lax matrices $T_D(z)$ parametrized by $\Lambda^+$-valued divisors $D$ on $\mathbb{P}^1$. To this end, we study the shifted Drinfeld Yangians $Y_\mu(\mathfrak{gl}_n)$ and quantum…

Let $G$ be a finite nilpotent group and $K$ a number field with torsion relatively prime to the order of $G$. By a sequence of central group extensions with cyclic kernel we obtain an upper bound for the minimum number of prime ideals of…

Lattice polyhedra $Q_1$ and $Q_2$ with the same tail cone are said to be normally located if every lattice point in the Minkowski sum $Q_1+Q_2$ is the sum of lattice points from $Q_1$ and $Q_2$, respectively. We prove that if the normal fan…

Let $G_n$ be the genus of a two-dimensional surface obtained by gluing, uniformly at random, the sides of an $n$-gon. Recently Linial and Nowik proved, via an enumerational formula due to Harer and Zagier, that the expected value of $G_n$…

Let $G$ be a connected, simply connected nilpotent group and $\pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(\mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $\pi$…

Let $k$ be a field. Let $X/k$ be a stable curve whose geometric irreducible components are smooth rational curves. Taking Stein factorization of its normalization, we get a conic. We show the conic is non-split in certain cases. As an…

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The…

We derive a formula for the entries of the (unitriangular) transition matrices between the standard monomial and dual canonical bases of the irreducible polynomial representations of U_q(gl_n) in terms of Kazhdan-Lusztig polynomials.

In this paper we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic $\ell>3$ as the Galois group of a tamely ramified Galois extension of $\mathbb{Q}$. The strategy is to consider the…

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…

In Part I of this article we generalize the Linearized Doubling (LD) approach, introduced in earlier work by NK, by proving a general theorem stating that if $\Sigma$ is a closed minimal surface embedded in a Riemannian three-manifold…

In this article, we prove that the Swan conductor of an \'etale sheaf on a smooth variety defined by Abbes and Saito's logarithmic ramification theory can be computed by its classical Swan conductors after restricting it to curves. It…

Investigations of monogenity and power integral bases were recently extended from the absolute case (over Q) to the relative case (over algebraic number fields). Formerly, in the relative case we only succeeded to calculate generators of…

Let $\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements and $\mathbb{F}_{q^n}$ its extension of degree $n$. We prove that there exists a primitive element of $\mathbb{F}_{q^n}$ that produces a completely normal basis…

We provide several new $q$-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric…

Let $C_{n,g}$ be the number of rooted cubic maps with $2n$ vertices on the orientable surface of genus $g$. We show that the sequence $(C_{n,g}:g\ge 0)$ is asymptotically normal with mean and variance asymptotic to $(1/2)(n-\ln n)$ and…

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Based on the previous results of the author, we can describe the Langlands parameter of an essentially tame supercuspidal representation…