Laboratoire Jean-Alexandre Dieudonné

Refined Chern characteristic classes of blow-ups

Abstract We prove a blow-up formula for refined Chern characteristic classes of compact complex manifolds. To this end, we establish a version of Riemann–Roch without denominators for the refined Chern characteristic classes. In particular, as an application, we study the behavio...

Metric and spectral aspects of random complex divisors

For any integer n\geq 2 , we prove that for any large enough integer d , with large probability the injectivity radius of a random degree d complex hypersurface in \mathbb{C}P^{n} is larger than {d^{-(n+2)/2}} . Here the hypersurface is endowed with the restriction of the ambient...

Ginzburg–Landau Minimizers with High Topological Degrees in an Annulus

Abstract. Motivated by recent experiments on fermionic rings, we study the asymptotic behavior of minimizers of the Ginzburg–Landau (GL) energy in an annulus with a Dirichlet data which depends on the GL parameter on the outer boundary. We show that there is a critical degree of...

Stochastic Optimal Control for Systems with Drifts of Bounded Variation: A Maximum Principle Approach

Abstract. We study a stochastic control problem for nonlinear systems governed by stochastic differential equations (SDEs) with irregular drift. The drift coefficient is assumed to decompose as [Formula: see text], where [Formula: see text] is bounded and Borel measurable, [Formu...

Noise through an Additional Variable for Mean Field Games Master Equation on Finite State Space

Abstract. This paper provides a mathematical study of the well-posedness of a master equation with terms modeling common noise on finite state space. In this setting, the solution of the master equation depends on an additional variable modeling the value of a stochastic process...