Related papers: The maximal decomposition of the Turaev-Viro TQFT

In this work we study the $E_{\infty}$-ring $\text{THH}(\mathbb{F}_p)$ as a graded spectrum. Following an identification at the level of $E_2$-algebras with $\mathbb{F}_p[\Omega S^3]$, the group ring of the $E_1$-group $\Omega S^3$ over…

We establish a connection between three-dimensional self-mirror symmetric $\mathcal N=4$ superconformal field theories (SCFTs) and time-reversal invariant topological quantum field theories (TQFTs) arising from universal mass deformations.…

We compute section class relative equivariant Gromov-Witten invariants of the total space of P^2-bundles of the form P(O+L1+L2)-->C where C is a genus g curve, O is the trivial bundle, and L1 (resp. L2) is an arbitrary line bundle of degree…

We prove the $r$-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer $r$: The 2-groupoid of 2-dimensional fully extended $r$-spin TQFTs with given target is equivalent to the homotopy fixed points of…

Teichm\"uller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context…

Let $G/H$ be a homogeneous variety, and let $X$ be a $G$-equivariant embedding of $G/H$such that the number of $G$-orbits in $X$ is finite. We show that the equivariant Borel-Moore homology of $X$ has a filtration with associated graded…

We describe a deformation of the $\infty$-category of Borel $G$-spectra for a finite group $G$. This provides a new presentation of the $a$-complete real Artin--Tate motivic stable homotopy category when $G=C_2$ and gives a new…

The universal Vassiliev-Kontsevich invariant is a functor from the category of tangles to a certain graded category of chord diagrams, compatible with the Vassiliev filtration and whose associated graded is an isomorphism. The Vassiliev…

In this paper, we introduce the Hessian-Schatten total variation (HTV) -- a novel seminorm that quantifies the total "rugosity" of multivariate functions. Our motivation for defining HTV is to assess the complexity of supervised-learning…

A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms…

We consider a cobordism category whose morphisms are punctured connect sums of $S^1 \times S^2$'s (wormhole spaces) with embedded admissibly colored banded trivalent graphs. We define a TQFT on this cobordism category over the field of…

We propose a field theoretic realization of the non-unitary $\mathfrak{sl}(2,\mathbb{C})$ Witten-Reshetikhin-Turaev Topological Quantum Field Theory(WRT TQFT). The WRT TQFT at the principal root of unity is unitary. It is known to be…

In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology…

We define a class of non-compact Fano toric manifolds, called admissible toric manifolds, for which Floer theory and quantum cohomology are defined. The class includes Fano toric negative line bundles, and it allows blow-ups along fixed…

We revisit and extend the Durdevic theory of complete calculi on quantum principal bundles. In this setting one naturally obtains a graded Hopf-Galois extension of the higher order calculus and an intrinsic decomposition of degree 1-forms…

It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant $T\bar{T}$ perturbation of dimension $4$ has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the…

We show that the path-integral of conformal field theories in $D$ dimensions (CFT$_D$) can be constructed by solving for eigenstates of an RG operator following from the Turaev-Viro formulation of a topological field theory in $D+1$…

To any affine scheme with a $\mathbb{G}_m$-action, we provide a Bousfield colocalization on the equivariant derived category of modules by constructing, via homotopical methods, an idempotent integral kernel. This endows the equivariant…

Let $\pi$ be a group. The aim of this paper is to construct the category of Yetter-Drinfeld modules over the quasi-Turaev group coalgebra $H=(\{H_\a\}_{\a\in\pi},\Delta,\varepsilon,S,\Phi)$, and prove that this category is isomorphic to the…

Let $W$ be the Weyl group of a split semisimple group $G$. Its Hecke category $\mathsf{H}_W$ can be built from pure perverse sheaves on the double flag variety of $G$. By developing a formalism of generalized realization functors, we…