Related papers: Lectures on invertible field theories

In this paper we study the topology of cobordism categories of manifolds with corners. Specifically, if {Cob}_{d,<k>} is the category whose objets are a fixed dimension d, with corners of codimension less than or equal to k, then we…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

Cobordism offers a unique perspective into the non-perturbative sector of string theory by demanding the absence of higher form global symmetries for quantum gravitational consistency. In this work we compute the spin cobordism groups of…

This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to…

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…

A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classification of all special surfaces where this is not the case, i.e. of surfaces possessing isometries which preserve the mean curvature, is known…

A notion of vector field cobordism for oriented manifolds was defined by B\"okstedt and Svane. We extend this notion to define complex section cobordism for almost complex manifolds. We then determine the complex section cobordism groups…

1+1 dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed and manageable expressions thanks to…

We study the symmetric monoidal 2-category of finite semisimple module categories over a symmetric fusion category. In particular, we study $E_n$-algebras in this 2-category and compute their $E_n$-centers for $n=0,1,2$. We also compute the…

We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…

I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…

Smith homomorphisms are maps between bordism groups that change both the dimension and the tangential structure. We give a completely general account of Smith homomorphisms, unifying the many examples in the literature. We provide three…

Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.

These lectures review some of the basic properties of $N=2$ superconformal field theories and the corresponding topological field theories. One of my basic aims is to show how the techniques of topological field theory can be used to…

Lectures presented at the 33rd Karpacz Winter School ``Duality: Strings and Fields'' briefly introducing dualities in four-dimensional quantum field theory, and summarizing results found in supersymmetric field theories. The first lecture…

It is well known that braided monoidal categories are the categorical algebras of the little two-dimensional disks operad. We introduce involutive little disks operads, which are Z/2Z-orbifold versions of the little disks operads. We…

We describe the explicit construction of configurations of several 10d string theories joining at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories, predicted by the Cobordism Conjecture. We…

This is the second paper of a series that develops a bordism-theoretic point of view on orientations in enumerative geometry. The first paper is arXiv:2312.06818. This paper focuses on those applications to gauge theory that can be…

We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by…

The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomology, Postnikov towers, the theory of "n-stuff", and…