Related papers: Quasi-constant characters: Motivation, classificat…

In the case of an almost simple algebraic group $G$ of type $G_2$ over a field of characteristic $p>0$ we study the cohomology modules of line bundles on the flag variety for $G$. Our main result is a complete determination of the vanishing…

We establish a condition for the perturbative stability of zero energy nodal points in the quasi-particle spectrum of superconductors in the presence of coexisting \textit{commensurate} orders. The nodes are found to be stable if the…

An irreducible character of a finite group $G$ is called quasi $p$-Steinberg character for a prime $p$ if it takes a nonzero value on every $p$-regular element of $G$. In this article, we classify the quasi $p$-Steinberg characters of…

In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…

Let $k$ be an algebraic closure of finite fields with odd characteristic $p$ and a smooth projective scheme $\mathbf{X}/W(k)$. Let $\mathbf{X}^0$ be its generic fiber and $X$ the closed fiber. For $\mathbf{X}^0$ a curve Faltings conjectured…

Let $\Sigma$ be a countable alphabet. For $r\geq 1$, an infinite sequence $s$ with characters from $\Sigma$ is called $r$-quasi-regular, if for each $\sigma\in\Sigma$ the ratio of the longest to shortest interval between consecutive…

For a finite dimensional vector space V of dimension n, we consider the incidence correspondence (or partial flag variety) X in P(V) x P(V*), parametrizing pairs consisting of a point and a hyperplane containing it. We completely…

Let $f: Y\to X$ be a morphism between smooth complex quasi-projective varieties and $Z$ be the closure of $f(Y)$ with $\iota: Z\to X$ the inclusion map. We prove that a. for any field $K$, there exist finitely many semisimple…

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalize these strategies by viewing any geodesic metric space as a…

We construct an extended oriented $(2+\epsilon)$-dimensional topological field theory, the character field theory $X_G$ attached to a affine algebraic group in characteristic zero, which calculates the homology of character varieties of…

Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $\rho: \pi_1(S)\to Sl(n, \mathbb{C})$ be a semisimple linear representation of $\pi_1(S)$ which is unipotent near…

Let $G$ be a countable group. We introduce several equivalence relations on the set ${\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\lambda_{G/H}$ associated to $H\in {\rm Sub}(G)$ and compare…

Recent work of Shareshian and Wachs, Brosnan and Chow, and Guay-Paquet connects the well-known Stanley-Stembridge conjecture in combinatorics to the dot action of the symmetric group $S_n$ on the cohomology rings $H^*(Hess(S,h))$ of regular…

We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…

We introduce quasi-BPS categories for twisted Higgs bundles, which are building blocks of the derived category of coherent sheaves on the moduli stack of semistable twisted Higgs bundles over a smooth projective curve. Under some condition…

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…

We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we…

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E…