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315
The space of stability conditions on the local projective plane
 Duke Math. J
"... ABSTRACT. We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component. We prove that this conne ..."
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Cited by 28 (3 self)
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ABSTRACT. We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component. We prove that this connected component is simplyconnected. We determine the group of autoequivalences preserving this connected component. Finally, we show that there is a submanifold isomorphic to the universal covering of a moduli space of elliptic curves with level structure, with the morphism given by solutions of PicardFuchs equations. This result is motivated by the notion of Πstability and by mirror symmetry. 1.
The Modular Degree, Congruence Primes, and Multiplicity One
"... The modular degree and congruence number are two fundamental invariants of an elliptic curve over the rational field. Frey and Müller have asked whether these invariants coincide. We find that the question has a negative answer, and show that in the counterexamples, multiplicity one (defined below) ..."
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Cited by 19 (10 self)
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The modular degree and congruence number are two fundamental invariants of an elliptic curve over the rational field. Frey and Müller have asked whether these invariants coincide. We find that the question has a negative answer, and show that in the counterexamples, multiplicity one (defined below) does not hold. At the same time, we prove a theorem about the relation between the two invariants: the modular degree divides the congruence number, and the ratio is divisible only by primes whose squares divide the conductor of the elliptic curve. We discuss the ratio even in the case where the square of a prime does divide the conductor, and we study analogues of the two invariants for modular abelian varieties of arbitrary dimension.
Transcendental obstructions to weak approximation on general K3 surfaces
 Adv. Math
"... Abstract. We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental BrauerManin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kin ..."
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Cited by 18 (6 self)
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Abstract. We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental BrauerManin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kinds of Brauer classes and cubic fourfolds. 1.
Maximum likelihood for matrices with rank constraints
, 2013
"... Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of deter ..."
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Cited by 11 (5 self)
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Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions. This led to the discovery of maximum likelihood duality between matrices of complementary ranks, a result proved subsequently by Draisma and Rodriguez.
A combinatorial formula for orthogonal idempotents in the 0Hecke algebra of the symmetric group
 Electron. J. Combin
, 2011
"... Abstract. Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the 0Hecke algebra of the symmetric group, CH0(SN). This construction is compatible with the branching from H0(SN−1) to H0(SN). Résumé. En s’ap ..."
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Cited by 11 (3 self)
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Abstract. Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the 0Hecke algebra of the symmetric group, CH0(SN). This construction is compatible with the branching from H0(SN−1) to H0(SN). Résumé. En s’appuyant sur le travail de P.N. Norton, nous donnons des formules combinatoires pour deux décompositions maximales de l’identité en idempotents orthogonaux dans l’algèbre de Hecke H0(SN) du groupe symétrique à q = 0. Ces constructions sont compatibles avec le branchement de H0(SN−1) à H0(SN).
ON THE REPRESENTATION THEORY OF FINITE JTRIVIAL MONOIDS
 SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE
, 2011
"... In 1979, Norton showed that the representation theory of the 0Hecke algebra admits a rich combinatorial description. Her constructions rely heavily on some triangularity property of the product, but do not use explicitly that the 0Hecke algebra is a monoid algebra. The thesis of this paper is tha ..."
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Cited by 11 (2 self)
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In 1979, Norton showed that the representation theory of the 0Hecke algebra admits a rich combinatorial description. Her constructions rely heavily on some triangularity property of the product, but do not use explicitly that the 0Hecke algebra is a monoid algebra. The thesis of this paper is that considering the general setting of monoids admitting such a triangularity, namely Jtrivial monoids, sheds further light on the topic. This is a step in an ongoing effort to use representation theory to automatically extract combinatorial structures from (monoid) algebras, often in the form of posets and lattices, both from a theoretical and computational point of view, and with an implementation in Sage. Motivated by ongoing work on related monoids associated to Coxeter systems, and building on wellknown results in the semigroup community (such as the description of the simple modules or the radical), we describe how most of the data associated to the representation theory (Cartan matrix, quiver) of the algebra of any Jtrivial monoid M can be expressed combinatorially by counting appropriate
Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces
 Comm. Pure Appl. Math
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The inverse moment problem for convex polytopes: Implementation access
, 2014
"... We give a detailed technical report on the implementation of the algorithm presented in [GLPR12] for reconstructing an Nvertex convex polytope P in Rd from the knowledge of O(Nd) its moments. ..."
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Cited by 10 (4 self)
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We give a detailed technical report on the implementation of the algorithm presented in [GLPR12] for reconstructing an Nvertex convex polytope P in Rd from the knowledge of O(Nd) its moments.
Fault Attacks Against emv Signatures
"... Abstract. At ches 2009, Coron, Joux, Kizhvatov, Naccache and Paillier (cjknp) exhibited a fault attack against rsa signatures with partially known messages. This attack allows factoring the public modulus N. While the size of the unknown message part (ump) increases with the number of faulty signatu ..."
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Cited by 9 (5 self)
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Abstract. At ches 2009, Coron, Joux, Kizhvatov, Naccache and Paillier (cjknp) exhibited a fault attack against rsa signatures with partially known messages. This attack allows factoring the public modulus N. While the size of the unknown message part (ump) increases with the number of faulty signatures available, the complexity of cjknp’s attack increases exponentially with the number of faulty signatures. This paper describes a simpler attack, whose complexity is polynomial in the number of faults; consequently, the new attack can handle much larger umps. The new technique can factor N in a fraction of a second using ten faulty emv signatures – a target beyond cjknp’s reach. We show how to apply the attack even when N is unknown, a frequent situation in reallife attacks.