Related papers: Higher categories of push-pull spans, II: Matrix f…
We introduce a new class of two dimensional conformal field theories by extending Wess-Zumino-Witten (WZW) models to chiral algebras with matrix-valued levels. The new CFTs are based on holomorphic currents with an operator product…
We describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We…
In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni, Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly more generalized notion of double categories allows us…
We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use "algebraic" characterizations of fibrations to produce factorizations…
We advocate a new approach to the study of unitary matrix models in external fields which emphasizes their relationship to Generalized Kontsevich Models (GKM) with non-polynomial potentials. For example, we show that the partition function…
The category of effective $Witt$-motives $DWM^-(k)$ with functor $WM\colon Sm_k\to DWM^-(k)$ defining motives of smooth affine varieties for perfect field $k$, $char k\neq 2$ is constructed. In the construction Voevodsky-Suslin method is…
In this paper, we describe a relation between a categorical quantization construction, called "2-linearization", and extended topological quantum field theory (ETQFT). We then describe an extension of the 2-linearization process which…
We study the structure of the category of representations of $\mathbf{FA}$, the category of finite sets and all maps, mostly working over a field of characteristic zero. This category is not semi-simple and exhibits interesting features. We…
This is a PhD Thesis on the connection between subfactors (more precisely, their corresponding fusion categories) and Conformal Field Theory (CFT). Besides being a mathematically interesting topic on its own, subfactors have also attracted…
We define the Grothendieck-Witt category over a fixed ground ring. In order to study the structure of this category, we introduce the general theory of Gysin functors and their associated categories of correspondences. The latter…
We define a normed matrix factorization category and a notion of bounding cochains for objects of this category. We classify bounding cochains up to gauge equivalence for spherical objects and use this classification to define numerical…
We continue study of some algebraic varieties (called resultantal varieties) started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions of Carlitz modules". These varieties are related with the…
We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-triangulated closed categories to such structures on some…
Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…
We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator which is given by the stabilization of the residue field. We deduce a…
We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and…
We consider the canonical Wiener-Hopf factorisation of $2 \times 2$ symmetric matrices $\mathcal M$ with respect to a contour $\Gamma$. For the case that the quotient $q$ of the two diagonal elements of $\mathcal M$ is a rational function,…
In this paper we give sufficient conditions for lifting an enhanced factorization system $ (\mathcal{E}, \mathcal{M}) $ on a $ 2 $-category $ \mathbf{D} $ to the functor $ 2 $-category $ \mathbf{D}^{\mathbf{C}} $, where $ \mathbf{C} $ is a…
Let $J$ be a set of pairs consisting of good modules over an affine quantum algebra and invertible elements. The distribution of poles of the normalized R-matrices yields Khovanov-Lauda-Rouquier algebras $R^J$. We define a functor $F$ from…
We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal category generated by one object and one endomorphism. This categorifies the ring of symmetric…