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Lectures on tensor categories and modular functors
Introduction Braided tensor categories Ribbon categories Modular tensor categories 3-dimensional topological quantum field theory Modular functor Moduli spaces and complex modular functor…
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Braided Tensor Categories and Extensions of Vertex Operator Algebras
Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided…
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LAURENT EXPANSIONS IN CLUSTER ALGEBRAS VIA QUIVER REPRESENTATIONS
We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit…
The universal rotation curve of spiral galaxies
The observed strong dark-to-luminous matter coupling is described by a bias relation between visible and dark matter sources. We discuss the bias which emerges in the case where the topological…
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On $G$--equivariant modular categories
In this paper, we study $G$-equivariant tensor categories for a finite group $G$. These categories were introduced by Turaev under the name of $G$-crossed categories; the motivating example of such a…
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On the polynomial invariants of the elasticity tensor
We consider the old problem of finding a basis of polynomial invariants of the fourth rank tensorC of elastic moduli of an anisotropic material. DecomposingC into its irreducible components we reduce…
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Infinite dimensional lie groups; their orbits, invariants and representations. The geometry of moments
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Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
Introduction Representations of finite-dimensional and affine Lie algebras Knizhnik-Zamolodchikov equations Solutions of the Knizhnik-Zamolodchikov equations Free field realization Quantum groups…
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Spherical functions on affine Lie groups
We describe vector valued conjugacy equivariant functions on a group K in two cases -- K is a compact simple Lie group, and K is an affine Lie group. We construct such functions as weighted traces…
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String-net model of Turaev-Viro invariants
TLDR
The relation between the Turaev--Viro TQFT and the string-net space introduced in the papers of Levin and Wen and the case of surfaces with boundary is considered in detail.
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