Related papers: A foamy approach to Soergel bimodules

In this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounded complexes in finite type A Soergel bimodules. This functor…

The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum $\mathfrak{sl}_2$ representation category. It also establishes a precise relation between the simple transitive…

These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…

In this note we make a minor correction to the paper ``Simplicial monoids and Segal categories."

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

The aim of this note is to prove the analogue of Poincar\'e duality in the chiral Hodge cohomology.

The aim of this work is to clarify the relationship between homology theory of commutative monoids constructed 'a la Quillen and technology of Gamma-modules.

Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups $\mathrm{SCG}$ are…

When a category is equipped with a 2-cell structure it becomes a sesquicategory but not necessarily a 2-category. It is widely accepted that the latter property is equivalent to the middle interchange law. However, little attention has been…

This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cl\'ery and Carel Faber.

We classify simple transitive $2$-representations of certain $2$-sub\-ca\-te\-go\-ri\-es of the $2$-category of Soergel bimodules over the coinvariant algebra in Coxeter types $B_2$ and $I_2(5)$. In the $I_2(5)$ case it turns out that…

These short lecture notes provide an introduction to some basic notions of F-theory with some special emphasis on its relation to Type IIB orientifolds with O7/O3-planes.

We use 4-valent planar graphs and singular cobordisms (called foams) to construct an integral doubly-graded cohomology for tangles, and in particular for links, whose graded Euler characteristic yields the sl(n) link polynomial (for n > 3).

In this paper we describe a general framework for constructing examples of locally linear semistrict monoidal 2-categories covering many examples appearing in link homology theory. The main input datum is a closed foam evaluation formula.…

The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type…

We produce Jucys-Murphy elements for the diagrammatical category of Soergel bimodules associated with general Coxeter groups, and use them to diagonalize the bilinear form on the cell modules. This gives rise to an expression for the…

Let $X$ be a partial flag variety, equipped with the Borel action by multiplication. We give a criterion for the equivariant derived category with modular coefficients to be formal.

Just as point objects are parallel transported along curves, giving holonomies, string-like objects are parallel transported along surfaces, giving surface holonomies. Composition of these surfaces correspond to products in a category…

In this note, we compute the split Grothendieck ring of a generalized category of Soergel bimodules of type $A_2$, where we take one generator for each reflection. We give a presentation by generators and relations of it and a…

In this paper we complete the $\mathrm{ADE}$-like classification of simple transitive $2$-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In particular, we use bipartite graphs and zigzag…