Related papers: Unital k-Restricted Infinity-Operads

We introduce a construction that associates, to each finite dimensional k-vector space V, a family of projective k-varieties that comes equipped with the structure of a operad in the category of k-schemes. When dim V = 1, this operad…

We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar…

We prove the existence of minimal models a la Sullivan for operads with non-trivial arity zero. So, up to homotopy algebras with strict units are just operad algebras over these minimal models. As an application we give another proof of the…

We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm convergence. This may be described more extensively as the…

We introduce the centred and the uncentred triangular maximal operators $\mathcal T$ and $\mathcal U$, respectively, on any locally finite tree in which each vertex has at least three neighbours. We prove that both $\mathcal T$ and…

We define a category $\mathsf{List}$ whose objects are sets and morphisms are mappings which assign to an element in the domain an ordered sequence (list) of elements in the codomain. We introduce and study a category of simplicial objects…

We provide a complete set of supersymmetric constraints for the anomalous dimensions of the conformal twist-two operators to all orders of perturbation theory. Employing them we derive new relations between the exclusive evolution kernels…

We prove that for a topological operad $P$ the operad of oriented cubical chains, $C^{ord}_\ast(P)$, and the operad of singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{ord}_\ast(P;\mathbb{Q})$ is formal if and only…

We show that in $K$-theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK$-theory are faithful if and only if they are faithful on…

We give a sufficient condition using the Ozsv\'ath-Stipsicz-Szab\'o concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on…

We define the notion of Cartesian 2-fibrations, and prove a weak analogue of straightening. Using Barwick's notion of operator categories and the notion of a Cartesian 2-fibration, we extend the notion of $\infty$-operads to the…

We initiate the classification of unitary superconformal defects in unitary superconformal field theories (SCFT) of diverse spacetime dimensions $3\leq d \leq 6$. Our method explores general constraints from the defect superconformal…

In this paper, we introduce a new notion of algebra over a linear $\infty$-operad and a corresponding notion of coalgebra over an $\infty$-cooperad. We next extend the Koszul duality between linear $\infty$-operads and linear…

We prove a version of Temkin's local altered uniformization theorem. We show that for any rig-smooth, quasi-compact and quasi-separated admissible formal $\mathcal{O}_K$-model $\mathfrak{X}$, there is a finite extension $K'/K$ such that…

We study the category of nonsymmetric dg operads valued in strict graded-mixed complexes, equipped with a distinguished arity zero weight one element which generates the weight grading, and whose differential has weight one. We show that…

We study two closely related operads: the Gelfand-Dorfman operad GD and the Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal algebra structure. We prove Koszulity of the Conformal Lie operad using the Groebner…

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_1$-functor without using the corresponding result from linear $K$-theory under the…

We give examples of rank-one transformations that are (weak) doubly ergodic and rigid (so all their cartesian products are conservative), but with non-ergodic $2$-fold cartesian product. We give conditions for rank-one infinite…

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…

We propose a construction of the monoidal envelope of $\infty$-operads in the model of Segal dendroidal spaces, and use it to define cocartesian fibrations of such. We achieve this by viewing the dendroidal category as a "plus construction"…