相关论文: Tensor triangular geometry -- Notes for an Oberwol…

We examine the concept of field in tensor-triangular geometry. We gather examples and discuss possible approaches, while highlighting open problems. As the construction of residue tt-fields remains elusive, we instead produce suitable…

These notes for a master class at Aarhus University (March 22--24, 2023) provide an introduction to the theory of completion for triangulated categories.

This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part III), we introduce and study…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…

We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms…

This is an informal set of lecture notes on moduli spaces of curves based on a set of lectures given at the ICTP last summer. It begins at an elementary level and discusses the genus 1 case in detail. The notes then give an informal…

This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…

In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.

In these notes, we describe several geometric interpretations of $H^2(X)$ when $X$ is a trisected 4-manifold. The main insight is that, by analogy with Hodge theory and sheaf cohomology in algebraic geometry, classes in $H^2(X)$ can be…

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…

These are notes for a Ph.D.\ course I held at SISSA, Trieste, in the Winter 2025. We review well-known topics in Riemannian geometry where Lie groups play a fundamental role. Part of the theory of compact connected Lie groups, their…

The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

We recall P. Balmer's definition of tensor triangular Chow group for a tensor triangulated category $\mathcal{K}$ and explore some of its properties. We give a proof that for a suitably nice scheme $X$ it recovers the usual notion of Chow…

Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…

These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…