Institut de Mathématiques de Jussieu-Paris Rive Gauche

Hyperbolicity and fundamental groups of complex quasi‐projective varieties (III): Applications

Abstract This paper is Part III of a series of three. We begin by introducing the notion of ‐special varieties, which can be seen as varieties “chain‐connected by the Zariski closures of entire curves.” We prove that if is either a special smooth complex quasi‐projective variety...

Some geometric applications of the discrete heat flow

We present two geometric applications of heat flow methods on the discrete hypercube { - 1 , 1 } n . First, we prove that if X is a finite-dimensional normed space, then the bi-Lipschitz distortion required to embed { - 1 , 1 } n equipped with the Hamming metric into X satisfies...

An Iterative Construction of Complete Kähler–Einstein Metrics

We extend Tsuji’s iterative construction of Kähler–Einstein metrics with negative scalar curvature to non-compact Kähler manifolds with bounded geometry, using Berndtsson’s method from the compact setting. Consequently, given a holomorphic surjective map p\colon X\to Y , where X...

On linearised and elliptic versions of the Kashiwara–Vergne Lie algebra

The goal of this article is to define a linearized or depth-graded version 𝔩𝔨𝔯𝔳 , and a closely related elliptic version 𝔨𝔯𝔳 ell , of the Kashiwara–Vergne Lie algebra 𝔨𝔯𝔳 originally constructed by Alekseev and Torossian as the space of solutions to the linearized Kashiwara–Vergne...

Improved convergence rates in the fast-reaction approximation of the triangular Shigesada-Kawasaki-Teramoto system

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension d ≤ 3. We provide explicit convergence rates on the whole domain in 𝐿 ∞ ⁢ 𝐿 2 ∩ 𝐿 2 ⁢ 𝐻 1 and in the interior we prove convergence with an...

Quantum propagation for Berezin–Toeplitz operators

We describe the asymptotic behaviour of the quantum propagator generated by a Berezin–Toeplitz operator with real-valued principal symbol. We also give precise asymptotics for smoothed spectral projectors associated with the operator in the autonomous case; this leads us to intro...

Characteristic cycle and wild Lefschetz theorems

Abstract By relying on a new approach to Lefschetz type questions based on Beilinson’s singular support and Saito’s characteristic cycle, we prove an instance of the wild Lefschetz theorem envisioned by Deligne. Our main tool are new finiteness results for the characteristic cycl...

Almost sure upper bound for random multiplicative functions

Let ε>0. Let f be a Steinhaus or Rademacher random multiplicative function. We prove that almost surely, as x→+∞, ∑n⩽xf(n)≪x√(log2x)3/4+ε.

Weak-Strong Uniqueness for the Landau Equation by a Relative Entropy Method

Abstract. We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in sta...

Differentiability of the Value Function in Control-Constrained Parabolic Problems

Abstract. Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional assumptions on the solution o...

The algebraic structures of social organizations: the operad of cooperative games

The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we start by endowing the collection of all...

Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators

We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak...

Pinwheels in symplectic rational and ruled surfaces and non‐squeezing of rational homology balls

Abstract We use almost toric fibrations and the symplectic rational blow‐up to determine when certain Lagrangian pinwheels, which we call liminal , embed in symplectic rational and ruled surfaces. The case of ‐pinwheels, namely Lagrangian , answers a question of Kronheimer in the...