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A geometric characterization of the upper bound for the span of the Jones polynomial
(World Scientific, 2011-07)
Let D be a link diagram with n crossings, sA and sB its extreme states and |sAD| (resp. |sBD|) the number of simple closed curves that appear when smoothing D according to sA (resp. sB). We give a general formula for the ...
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Irregular Hodge filtration of some confluent hypergeometric systems
(Cambridge University Press, 2019-05-24)
We determine the irregular Hodge filtration, as introduced by Sabbah, for the purely irregular hypergeometric D-modules. We obtain, in particular, a formula for the irregular Hodge numbers of these systems. We use the ...
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Echelons of power series and Gabrielov’s counterexample to nested linear Artin Approximation
(London Mathematical Society, 2018)
Gabrielov’s famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization ...
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Reducible braids and Garside theory
(Geometry & Topology Publications, 2011)
We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a ...
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Polynomial braid combing
(Oxford University Press, 2018)
We prove that, for n ≥ 3, the minimal dimension of a model of the classifying space of the braid group Bn, and of the pure braid group Pn, with respect to the family of virtually cyclic groups is n.
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Sur l’irréductibilité d’une induite parabolique
(De Gruyter, 2009)
Let F be a non-Archimedean locally compact field and let D be a central division algebra over F. Let p1 and p2 be respectively two smooth irreducible representations of GLðn1; DÞ and GLðn2; DÞ, n1; n2 f0. In this article, ...
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Alexander-Conway polynomial state model and link homology
(World Scientific Publishing, 2016-03)
This paper shows how the Formal Knot Theory state model for the Alexander-Conway polynomial is related to Knot Floer Homology. In particular we prove a parity result about the states in this model that clarifies certain ...
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Examples of hypergeometric twistor D-modules
(Mathematical Sciences Publishers, 2019-08-18)
We show that certain one-dimensional hypergeometric differential systems underlie objects of the category of irregular mixed Hodge modules, which was recently introduced by Sabbah, and compute the irregular Hodge filtration ...
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On reduction curves and Garside properties of braids
(American Mathematical Society, 2011)
In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. ...
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On the ubiquity of trivial torsion on elliptic curves
(Springer, 2010-08)
The purpose of this paper is to give a down-to-earth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.