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Adv Math (N Y) 2020 ;14(1)

Computer Security Division, National Institute of Standards and Technology Gaithersburg, MD 20899, USA.

This article introduces the NIST post-quantum cryptography standardization process. We highlight the challenges, discuss the mathematical problems in the proposed post-quantum cryptographic algorithms and the opportunities for mathematics researchers to contribute. Read More

Adv Math (N Y) 2013 Nov;247(100):103-122

Fakultät für Mathematik, Universität Wien, Vienna, Austria.

Let be a unimodular Lie group, a compact manifold with boundary, and the total space of a principal bundle [Formula: see text] so that is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point [Formula: see text] such that [Formula: see text] is contained in the complex tangent space [Formula: see text] of at , then the Bergman space of is large. Natural examples include the gauged -complexifications of Heinzner, Huckleberry, and Kutzschebauch. Read More

Adv Math (N Y) 2013 Aug;243(100):232-261

Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA ; Fakultät für Mathematik, Universität Wien, 1090 Wien, Austria.

This paper presents a new approach to the dimension theory of triangulated categories by considering invariants that arise in the pretriangulated setting. Read More

Adv Math (N Y) 2012 Jun;230(3):978-994

University of Salzburg, Hellbrunner Strasse 34, 5020 Salzburg, Austria.

A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used to obtain a family of Brunn-Minkowski type inequalities for rigid motion intertwining Minkowski valuations. Read More

Adv Math (N Y) 2012 Jun;230(3):819-838

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, A-4040 Linz, Austria.

In 1994, James Sellers conjectured an infinite family of Ramanujan type congruences for 2-colored Frobenius partitions introduced by George E. Andrews. These congruences arise modulo powers of 5. Read More

Adv Math (N Y) 2012 Jan;229(2):935-967

Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.

We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and replace the cycle space of a graph by a new homology group for continua which is a quotient of the first singular homology group [Formula: see text]. This homology seems to be particularly apt for studying spaces with infinitely generated [Formula: see text], e. Read More

Adv Math (N Y) 2011 Jan;226(1):139-175

LIRMM, CNRS UMR 5506, Université Montpellier II, 161 rue Ada, 34392 Montpellier Cedex 5, France ; LIAFA, CNRS UMR 7089, Université Paris Diderot - Paris 7, Case 7014, 75205 Paris Cedex 13, France.

Shift radix systems form a collection of dynamical systems depending on a parameter which varies in the -dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. Read More