Related papers: The Rost invariant has zero kernel for quasi-split…

We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…

In the present article we investigate ordinary and equivariant Rost motives. We provide an equivariant motivic decomposition of the variety X of full flags of a split semisimple algebraic group over a smooth base scheme, study torsion…

We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independent random walks. Firstly, we generalise a celebrated…

The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show that the combination of the core group and its peripheral…

The goal of this paper is to provide a methodology to prove existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same…

We fill a gap pointed out by N. Sheridan in the proof of independence of genus zero Gromov-Witten invariants from the choice of divisor in the Cieliebak-Mohnke perturbation scheme.

For any simple complex Lie algebra $\mathfrak{g}$, we show that the degrees of the "ADO" link polynomials coming from the unrolled restricted quantum group $\overline{U}^H_q(\mathfrak{g})$ at a root of unity give lower bounds to the Seifert…

For a certain class of real analytic varieties with Lie group actions we develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, we construct a…

To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of…

We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the…

We prove the Berenstein-Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite dimensional simple algebraic groups admit quantum cluster algebra structures with initial seeds as specified by [4].…

We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and…

In this article, we study the change of genus zero Gromov-Witten invariants under Type II extremal transitions in degree 4.

We study algebraic dynamical systems (and, more generally, $\sigma$-varieties) $\Phi:{\mathbb A}^n_{\mathbb C} \to {\mathbb A}^n_{\mathbb C}$ given by coordinatewise univariate polynomials by refining a theorem of Ritt. More precisely, we…

We prove a recent conjecture of Manolescu-Willis which states that the $s$-invariant of a knot in $\mathbb{RP}^3$ (as defined by them) gives a lower bound on its null-homologous slice genus in the unit disk bundle of $TS^2$. We also…

Let $V$ be a symmetric space over a connected reductive Lie algebra $G$, with Lie algebra $\mathfrak{g}$ and discriminant $\delta\in \mathbb{C}[V]$. A fundamental object is the invariant holonomic system $\mathcal{G} =\mathcal{D}(V)\Big/…

We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated a la Arthur multiplied by the absolute value of the determinant to the power $s…

In this article, we study $G$-covers of klt varieties, where $G$ is a reductive group. First, we exhibit an example of a klt singularity admitting a $\mathbb{P}{\rm GL}_n(\mathbb{K})$-cover that is not of klt type. Then, we restrict…

We study orbifold Gromov--Witten invariants of the $r$-th root stack $X_{D,r}$ with a pair of mid-ages when $r$ is sufficiently large. We prove that genus $g$ invariants with a pair of mid-ages $k_a/r$ and $1-k_a/r$ are polynomials in $k_a$…

In this article, we describe a simple covariant characterisation of initial data sets which give rise to Petrov type D vacuum spacetime developments. As an application, we derive an integral invariant which, when restricted to the…