相关论文: HKR characters and higher twisted sectors

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…

The purpose of this paper is twofold. We explore higher property T as an abstract group-theoretic property. In particular, we provide new operator-algebraic characterizations of higher property T. Then we turn to lattices in semisimple Lie…

We explicitly construct generators of the rational homotopy groups of the space of stable h-cobordisms of the classifying space of a cyclic group of order n by generalizing a construction of Hatcher. This result will be used in a separate…

We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.

In this article we shall study the analytic theory and the representation theoretic interpretations of Hankel transforms and fundamental Bessel kernels of an arbitrary rank over an archimedean field.

We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.

Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

This rough note describes some attempts to define a notion of enriched topology (and the associated theory of enriched stacks) on a category enriched over a symmetric monoidal model category, and poses some related questions.

We describe integral lifts K(L), indexed by local fields L of degree n = [L:\Q_p], of the extraordinary cohomology theories K(n), and apply the generalized character theory of Hopkins, Kuhn and Ravenel to identify K(L)(BG) \otimes \Q$, for…

We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We…

Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy…

In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha…

Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied…

This paper is mainly about an early result that the orbifold stack is globally representable via some $ \infty $-categorical techniques.

In this expository article, we give a gentle introduction to the Erd\H{o}s-R\'enyi random graphs and threshold phenomena that they exhibit. We also mildly introduce the Kahn-Kalai Conjecture with several intuitive examples, mainly targeting…

This sketch argues that work of Hesselholt on the topological Hochschild homology of $\Cp$ extends, using work of Scholze and others, to define complex orientations for a version of topological Hochschild homology for rings of integers in a…