We prove that character sheaves of a reductive group defined over any characteristic have nilpotent singular support, partially extending the work of [5, 16] to positive characteristic. We do this by introducing a category of tame perverse sheaves and studying its properties.

This work deals with the finite element approximation of a prestressed shell model in the case of isometrically deformed shell. Using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirm the efficiency of our residual a posteriori estimator.

We study the density of half-horocycles or half-orbits of the horocyclic flow on the unit tangent bundle of geometrically infinite hyperbolic surfaces. In [10] Schapira proved that under some assumptions, both half-horocycles (h s v) s≥0 and (h s v) s≤0 are simultaneously dense or not in the nonwandering set of the horocyclic flow. We construct a counterexample, when the assumptions are not satisfied, on a surface of first kind, answering a question of Schapira [10].

The construction of a random continuum 𝒞 from independent two-sided Brownian motions as considered in [11] almost surely yields a non-degenerate indecomposable continuum. We show that 𝒞 is not-hereditarily indecomposable and, in particular, it is (unfortunately) not the pseudo-arc.

This paper combines new and known results in a single convenient source for anyone interested in learning about quasi-linear functionals on locally compact spaces. We define singly generated subalgebras in different settings and study signed and positive quasi-linear functionals. Quasi-linear functionals are, in general, nonlinear, but linear on singly generated subalgebras. The paper gives representation theorems for quasi-linear functionals on C c (X), for bounded quasi-linear functionals on C 0 (X) on a locally compact space, and for quasi-linear functionals on C(X) on a compact space. There is an order-preserving bijection between quasi-linear functionals and compact-finite topological measures, which is also “isometric” when topological measures are finite. We present many properties of quasi-linear functionals and give an explicit example of a quasi-linear functional on ℝ 2 . Results of the paper will be helpful for further study and application of quasi-linear functionals in different areas of mathematics, including symplectic geometry.

We prove that every birational action of a group with Property FW can be regularized.

We study the long time behaviour of a dynamical system strongly linked to the nondiffusive scheme of Després and Lagoutiere for the 1-dimensional transport equation. This scheme is nondiffusive in the sense that discontinuities are not smoothened out through time. Numerical simulations indicate that the scheme error is uniformly bounded with time. We prove that this scheme is overcompressive when the Courant–Friedrichs–Levy number is 1/2: when the initial data is nondecreasing, the approximate solution becomes a Heaviside function. In a special case, we also understand how plateaus are formed in the solution and their stability, a distinctive feature of the Després and Lagoutière scheme.

We study the parabolically induced complex representations of the unitary group in 5 variables,U(5), defined over a p-adic field.Let F be a p-adic field. Let E:F be a field extension of degree two. U(5) has three proper standard Levi subgroups, the minimal Levi subgroup M 0 ≅E * ×E * ×E 1 and the two maximal Levi subgroups M 1 ≅GL(2,E)×E 1 and M 2 ≅E * ×U(3).We consider representations induced from M 0 , representations induced from non-cuspidal, not fully-induced representations of M 1 and M 2 and representations induced from cuspidal representations of M 1 .We determine the points and lines of reducibility and the irreducible subquotients of these representations. Further we describe - except several particular cases - the unitary dual in terms of Langlands quotients.

We attach buildings to modular lattices of finite length and show that they yield a natural framework for a metric version of the Harder-Narasimhan formalism. We establish a sufficient condition for the compatibility of Harder-Narasimhan filtrations with tensor products and verify our criterion in various cases coming from p-adic Hodge theory.

Schanuel’s conjecture states that the transcendence degree over ℚ of the 2n-tuple (λ 1 ,⋯,λ n ,e λ 1 ,⋯,e λ n ) is at least n for all λ 1 ,⋯,λ n ∈ℂ which are linearly independent over ℚ; if true it would settle a great number of elementary open problems in number theory, among which the transcendence of e over π.