Related papers: A Wonderful Embedding of the Loop Group

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…

(One typo corrected and one incorrect statement removed. Extra details on conserved quantities and symmetry algebras added).

This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.

This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…

The paper presents an enriched categorical account of homological perturbation theory, including the formulation, proof and functoriality properties of the homological perturbation lemma.

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.

We provide an axiomatic framework for working with a wide variety of closure operations on ideals and submodules in commutative algebra, including notions of reduction, independence, spread, and special parts of closures. This framework is…

Part A: A revised version of the guide in "Cardinal Arithmetic" ([Sh:g]), with corrections and expanded to include later works. Part B: Corrections to [Sh:g]. Part C: Contains some revised proof and improved theorems. Part D: Contains a…

This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.

We provide the spherical systems of the wonderful reductive subgroups of any reductive group.

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

Major changes in Sec. II (with much stronger estimates), minor changes in remaining sections, a new title. Deleted Appendix, added 2 new references.

These are notes from the lectures I gave at the Oberwolfach seminar `Tensor Triangular Geometry and Interactions' which was held in October 2025. The aim of these notes is to give an introduction to tensor triangular geometry, for both…

We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…

This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main change is that results about $\pi_1({\rm Diff}(M))$ are replaced…

This paper surveys some recent results, concerning the intrinsicness of natural subcategories of weakly approximable triangulated categories. We also review the results about uniqueness of enhancements of triangulated categories, with the…

The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifold in terms of linear symplectic geometry and exposes the…

We point out some minor errors in a paper by the first author, and explain why they do not affect the main results in the paper.

We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…

On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…