相关论文: sl(3)-Foams and the Khovanov-Lauda categorificatio…

Generalizing deformation quantizations with separation of variables of a K\"ahler manifold $M$, we adopt Fedosov's gluing argument to construct a category $\mathsf{DQ}$, enriched over sheaves of $\mathbb{C}[[\hbar]]$-modules on $M$, as a…

We find two natural spherical functors associated to the Kummer surface and analyse how their induced twists fit with Bridgeland's conjecture on the derived autoequivalence group of a complex algebraic K3 surface.

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le-Murakami-Ohtsuki invariant of homology three-spheres to a functor from the…

In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category…

In this paper, we show that any 3-dimensional normal affine quasihomogeneous SL(2)-variety can be described as a categorical quotient of a 4-dimensional affine hypersurface. Moreover, we show that the Cox ring of an arbitrary 3-dimensional…

In this paper we survey methods and results of classification of $k$-forms (resp. $k$-vectors on ${\bf R}^n$), understood as description of the orbit space of the standard ${\bf GL}(n, {\bf R})$-action on $\Lambda^k {\bf R}^{n*}$ (resp. on…

We extend the $sl(3)$-polynomial invariant for links to tangles. Motivated by Kuperberg's construction of this invariant via planar trivalent graphs, we first define a category of $sl(3)$ webs and its sister linear category, and describe…

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…

In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies…

We study ring of functions on the (classical and quantized) phase space of 2-dimensional BF theory with the gauge group $\mathrm{GL}_N$ coupled to a 1-dimensional quantum mechanics with global symmetry $\mathrm{GL}_K$. These functions are…

The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.

We study lax functors between bicategories as a generalized concept of monads and describe generalized notions and theorems of formal monad theory for lax functors. Our first approach is to use the 2-monad whose lax algebras are lax…

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are…

We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global…

This is a follow-up to the paper in which we categorified the affine quantum Schur algebra S(n,r) for 2 < r < n, using a quotient of Khovanov and Lauda's categorification of the affine quantum sl_n. In this paper we categorify S(n,n) for n…

This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of…

We categorify the idempotented form of quantum sl(n).

We give a construction of ``quantum Maslov characteristic classes'', generalizing to higher dimensional cycles the Hu-Lalonde-Seidel morphism. We also state a conjecture extending this to an $A _{\infty}$ functor from the exact path…

We construct an explicit equivalence between the (bi)category of gl(2) webs and foams and the Bar-Natan (bi)category of Temperley-Lieb diagrams and cobordisms. With this equivalence we can fix functoriality of every link homology theory…