Institut de Mathématiques de Jussieu-Paris Rive Gauche

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...