Related papers: Surface Drinfeld Torsors I : Higher Genus Associat…

We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the…

In his PhD thesis, Goosen combined the string-net and the generators-and-relations formalisms for arbitrary once-extended 3-dimensional TQFTs. In this paper we work this out in detail for the simplest non-trivial example, where the…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. In Part 2 we use this new theory together with our previous…

To each Drinfeld module over a finitely generated field with generic characteristic, one can associate a Galois representation arising from the Galois action on its torsion points. Recent work of Pink and R\"utsche has described the image…

We introduce a Grothendieck group of algebraic stacks (with affine stabilisers) analogous to the Grothendieck group of algebraic varieties. We then identify it with a certain localisation of the Grothendieck group of algebraic varieties.…

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain $U_q(gl(1|1))$ representations. Under this identification, up to a scalar factor, the map on the Grothendieck group induced by the tangle…

To distinguish the contributions to the generalized Hurwitz number of the source Riemann surface with different genus, we define the genus expanded cut-and-join operators by observing carefully the symplectic surgery and the gluing formulas…

We establish the functional relations between generating series of higher-order free cumulants and moments in higher-order free probability, solving an open problem posed fifteen years ago by Collins, Mingo, \'Sniady and Speicher. We…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

We study a relation between the Drinfeld modules and the even dimensional noncommutative tori. A non-abelian class field theory is developed based on this relation. Explicit generators of the Galois extensions are constructed.

This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general…

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field…

Consider a Frobenius kernel G in a split semisimple algebraic group, in very good characteristic. We provide an analysis of support for the Drinfeld center Z(rep(G)) of the representation category for G, or equivalently for the…

We revisit a construction principle of Fredholm operators using Hilbert complexes of densely defined, closed linear operators and apply this to particular choices of differential operators. The resulting index is then computed with the help…

Compared with algebraic varieties the local monodromy of Drinfeld modules appears to be hopelessly complex: The image of the wild inertia subgroup under Tate module representations is infinite save for the case of potential good reduction.…

Huang, Lepowsky and Zhang have developed a module theory for vertex operator algebras that endows suitably chosen module categories with the structure of braided monoidal categories. Included in the theory is a functor which assigns to…