Related papers: Variations on Van Kampen's method

We construct new examples of singular projective plane curves whose complements have finite and non-abelian fundamental groups, by generalizing the classical three cuspidal quartic curve discovered by Zariski.

Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…

We compute the topological Witt groups of every complex flag manifold of ordinary type, and thus the interesting (i.e. torsion) part of the KO-groups of these manifolds. Equivalently, we compute Balmer's Witt groups of each flag variety of…

A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are…

The paragrassmann calculus proposed earlier is applied to constructing paraconformal transformations and paragrassmann generalizations of the Virasoro-Neveu-Schwarz-Ramond algebras.

We discuss methods for using the Weil polynomial of an isogeny class of abelian varieties over a finite field to determine properties of the curves (if any) whose Jacobians lie in the isogeny class. Some methods are strong enough to show…

In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…

We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…

This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…

In "Proving that a genus 2 curve has complex multiplication", van Wamelen lists 19 curves of genus two over $\mathbf{Q}$ with complex multiplication (CM). For each of the 19 curves, the CM-field turns out to be cyclic Galois over…

We present new representations of Gauss--Legendre polynomials and their derivatives in the shifted power basis and in bases related to symmetric orthogonal Jacobi polynomials. Using these representations and certain recurrence relations, we…

We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…

Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.

Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…

We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that the generating function always satisfies a linear differential…

Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.

An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant…