相关论文: K-Theory Past and Present

Based on past contributions by Robert Schrader and Michael Karowski I review the problem of existence of interacting quantum field theory and present recent ideas and results on rigorous constructions.

This is a write-up of a two hour talk at the Simons workshop. It contains an elementary introduction to F-theory and may be useful for people new to the subject.

We provide a homotopy theorist's point of view on $KK$- and $E$-theory for $C^{*}$-algebras. We construct stable $\infty$-categories representing these theories through a sequence of Dwyer-Kan localizations of the category of…

The theory of rare $K$ decays is reviewed, emphasizing short-distance processes and the prospects to probe the physics of flavour. A brief overview of the subject is presented, along with a more detailed discussion of the theory of…

An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

Invited contribution to Annalen der Physik (Expert Opinion).

This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.

Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the…

In this paper we identify the ``nil-terms'' for Waldhausen's algebraic K-theory of spaces functor as the reduced K-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.

This is an appendix to the paper {\bf Asymptotic K-theory for groups acting on $\tA_2$ buildings}, and contains the results of the computations performed by the authors.

This is a survey article about some of the work of Peter Scholze for the Jahresbericht der DMV. No originality is claimed. It is hoped that it can serve as a guideline to an exciting and increasingly large edifice of theory.

We give a short biographical sketch of Karl Weierstrass.

This paper contains my recollection of the creation and development of the so-called BFKL approach and my ideas about the ways of its further development.

For a field $k$ we compute the $K$-theory of the exact category of $k[t_1,\dots,t_n]$-modules that are finite-dimensional over $k$, generalising the work of Kelley and Spanier.

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.

In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…

In this expository paper, we revisit the results of Atiyah-Singer and de Concini-Procesi-Vergne concerning the structure of the K-theory groups K_G(T_G M).

The story of (Ward-)Takahashi relations and their impact on physical theory is reviewed.

We build on work of Muro-Raptis in [Ann. K-Theory 2 (2017), no. 2, 303-340] and Cisinski-Neeman in [Adv. Math. 217 (2008), no. 4, 1381-1475] to prove that the additivity of derivator K-theory holds for a large class of derivators that we…