相关论文: The Operadic Nerve, Relative Nerve, and the Grothe…

The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other…

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the…

We show that the Whittaker functor on a regular block of the BGG-category $\mathcal{O}$ of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Mili\v{c}i\'{c}'s equivalence…

We show that if we start from a symmetric lower semi-bounded Schr\"odinger operator $\mathcal{H}$ on finitely supported functions on a discrete weighted graph (satisfying certain conditions), apply the Friedrichs construction to get a…

This lecture series is based on joint work in progress with Shaul Barkan, as well as work in progress of the author. The five sections of these notes correspond to the five lectures, but more details have been added. $2$-dimensional…

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{\underline{Re}p}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and…

The smash product construction (or the Grothendieck construction) takes a functor (or prestack) $F \colon B^{op} \to \mathbf{Cat}$ and returns a fibration $p \colon A \to B$. In this paper, we develop an analogue of the smash product for…

From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this…

This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…

Given a simplicial complex and a collection of subcomplexes covering it, the nerve theorem, a fundamental tool in topological combinatorics, guarantees a certain connectivity of the simplicial complex when connectivity conditions on the…

As shown by S. Eilenberg and J.C. Moore (1965), for a monad $F$ with right adjoint comonad $G$ on any catgeory $\mathbb{A}$, the category of unital $F$-modules $\mathbb{A}_F$ is isomorphic to the category of counital $G$-comodules…

Noncommutative (NC) gravity is constructed on the canonical noncommutative (Moyal-Weyl) space-time as a noncommutative $SO(2,3)_\star$ gauge theory. The NC gravity action consists of three different terms: the first term is of Mac-Dowell…

We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation…

We produce an indexed version of the Grothendieck construction. This gives an equivalence of categories between opfibrations over a fixed base in the 2-category of 2-copresheaves and 2-copresheaves on the Grothendieck construction of the…

In these notes, we define a new simplicial structure on a connected multiplicative operad and call it connected multiplicative simplicial operad (for short; simplicial operad). Next we introduce on this simplicial operad a brace algebra…

Let $A$ be a commutative algebra in a braided monoidal category $\mathcal{C}$; e.g., $A$ could be an extension of a vertex operator algebra (VOA) $V$ in a category $\mathcal{C}$ of $V$-modules. We study when the category $\mathcal{C}_A$ of…

For any Lie algebra of classical type or type $G_2$ we define a $K$-theoretic analog of Dunkl's elements, the so-called truncated {\it Ruijsenaars-Schneider-Macdonald elements}, $RSM$-elements for short, in the corresponding {\it…

We examine the categorical structure of the Grothendieck construction $\Sigma_{\mathsf{C}}\mathsf{L}$ of an indexed category $\mathsf{L} \colon \mathsf{C}^{op} \to \mathsf{CAT}$. Our analysis begins with characterisations of fibred limits,…

In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid…

We study the problem of recognizing whether a given abstract simplicial complex $K$ is the $k$-skeleton of the nerve of $j$-dimensional convex sets in $\mathbb{R}^d$. We denote this problem by $R(k,j,d)$. As a main contribution, we unify…