相关论文: Finite Type Invariants

Finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal invariant with integer coefficients based on the Magnus…

This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.

We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.

Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…

This is a review for Elsevier's Encyclopedia of mathematical physics.

We explore a family of invariants obtained from linking numbers. This is a family of Kauffman finite type invariants.

In this survey article for the Encyclopedia of Mathematical Physics, 2nd Edition, I give an introduction to quantum character varieties and quantum character stacks, with an emphasis on the unification between four different approaches to…

PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.

Computations in the cohomology of finite groups.

These lecture notes provide an elementary introduction, within the framework of finite quantum systems, to recent developments in the theory of entropic fluctuations.

We establish the ultra-violet finiteness of various classes of noncommutative gauge theories.

We present new classes of permutation polynomials over finite fields.

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…

Electronic version of Entry in Encyclopedia of Nonlinear Science.

We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.

Lectures on Poincare invariant quantum theory presented at TJNAF.

For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.

In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.