Reports de recerca
Recent Submissions
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Limit distribution of Hodge spectral exponents of irreducible plane curve singularities
(2024-05-07)
Research report
Open AccessWe study the distribution of the Hodge spectral exponents of an irreducible plane curve by comparing it with a continuous distribution. We provide a closed formula for this difference in terms of numerical invariants of ... -
Multiplier ideals of meromorphic functions in dimension two
(2024-05-08)
Research report
Open AccessWe providean effective method to compute multiplier ideals of meromorphic functions in dimension two. We also prove that meromorphic functions only have integer jumping numbers after reaching some threshold. -
Topological entropy of Turing complete dynamics
(2024-04-10)
Research report
Open AccessWe explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call “regular Turing machines” (which includes most of ... -
sVote with control components voting protocol: computational proof of complete verifiability and privacy
(2022-11-07)
Research report
Open AccesssVote with Control components is a cryptographic voting protocol that provides complete verifiability and guarantees voting secrecy and the non-disclosure of early provisional results. This report demonstrates that sVote ... -
Splitting of separatrices for rapid degenerate perturbations of the classical pendulum
(2023-02-16)
Research report
Open AccessIn this work we study the splitting distance of a rapidly perturbed pendulum H(x, y, t) = 1 2 y 2 + (cos(x) - 1) + µ(cos(x) - 1)g t e with g(t ) = P |k|>1 g [k] e ikt a 2p-periodic function and µ, e 1. Systems of this ... -
The Arnold conjecture for singular symplectic manifolds
(2022-12-02)
Research report
Open AccessIn this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of bm-symplectic manifolds. More precisely, we prove a lower bound on the number 1-periodic ... -
How to avoid repetitions in lattice-based deniable zero-knowledge proofs
(2022-06-23)
Research report
Open AccessInteractive zero-knowledge systems are a very important cryptographic primitive, used in many applications, especially when deniability (also known as non-transferability) is desired. In the lattice-based setting, the ... -
Rank axioms and supersimplicity
(2022-02-13)
Research report
Open AccessJust as Lascar’s notion of abstract rank axiomatizes the U rank, we propose axioms for the ranks SUd and SUf , the foundation ranks of dividing and forking. We study the relationships between these axioms. As with superstable, ... -
A b-symplectic slice theorem
(2020-09)
Research report
Open AccessIn this article, motivated by the study of symplectic structures on manifolds with bound-ary and the systematic study ofb-symplectic manifolds started in [10], we prove a slice theorem forLie group actions onb-symplectic manifolds -
Rigidity of cotangent lifts and integrable systems
(2020-05)
Research report
Open AccessIn this article we generalize a theorem by Palais on the rigidity ofcompact group actions to cotangent lifts. We use this result to prove rigidity forintegrable systems on symplectic manifolds including sytems with ... -
b-Structures on Lie groups and Poisson reduction
(2020-09)
Research report
Open AccessWe introduce the notion of b-Lie group as a pair(G, H) where Gis a Lie group and H is a codimension-one Lie subgroup, and study the associated canonical b-symplectic structure on the b-cotangent bundle bT*G together with ... -
Integrable systems on singular symplectic manifolds: from local to global
(2020-09)
Research report
Open AccessIn this article we consider integrable systems on manifolds endowed with singular sym-plectic structures of order one. By singular symplectic structures of order one we mean structureswhich are symplectic away from an ...
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