13 citations · 36 across the 11 of their papers we have counts for
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Mixed Hodge structures for vanishing cycles and orbifold cohomology
Antoine Douai
Above a Laurent polynomial f one makes grow a vector space of vanishing cycles (after the work of Sabbah, singularity setting), a graded Milnor ring (after the work of Kouchnirenko…
From Hodge theory for tame functions to Ehrhart theory for polytopes
Antoine Douai
We study the interplay between Sabbah's mixed Hodge structure for regular functions and Ehrhart theory for polytopes. To this end, we analyze the properties of the Poincaré polynom…
Hard Lefschetz properties and distribution of spectra in singularity theory and Ehrhart theory
Antoine Douai
We discuss the distribution of the spectrum at infinity of a convenient and nondegenerate Laurent polynomial (singularity side) and the distribution of the Newton spectrum of a pol…
A note on the toric Newton spectrum of a polynomial
Antoine Douai
We define the toric Newton spectrum of a polynomial and we give some applications in singularity theory, combinatorics and mirror symmetry.
Global spectra, polytopes and stacky invariants
Antoine Douai
Given a convex polytope, we define its geometric spectrum, a stacky version of Batyrev's stringy E-functions, and we prove a stacky version of a formula of Libgober and Wood about…
Quantum differential systems and some applications to mirror symmetry
Antoine Douai
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situ…