Related papers: Integrating quantum groups over surfaces
We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a…
This thesis contains various results on unitary 2-representations of finite groups and their 2-characters, as well as on pivotal structures for fusion categories. The motivation is extended topological quantum field theory (TQFT), where the…
This paper contains three related groupings of results. First, we consider a new notion of an admissible skein module of a surface associated to an ideal in a (non-semisimple) pivotal category. Second, we introduce the notion of a chromatic…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface frequently arise in enumerative problems. We use the K-theoretic Donaldson-Thomas theory of certain toric Calabi-Yau threefolds to…
The original definition of cluster algebras by Fomin and Zelevinsky has been categorified and generalised in several ways over the course of the past 20 years, giving rise to cluster theory. This study lead to Iyama and Yang's generalised…
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always…
We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…
We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
We determine the $d+1$ dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for $d$-dimensional QFTs obtained by compactifying M-theory on a non-compact space $X$. The resulting theory,…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\bf Z}_2$. Along the same way as the orbifold construction, we…
We show that interval partition functions (transition amplitudes) of three-dimensional $N = 2$ theories admit factorizations into sums of products of hemisphere partition functions with additional normalization factors. We prove the…
We show that topological strings on a class of non-compact Calabi-Yau threefolds is equivalent to two dimensional bosonic U(N) Yang-Mills on a torus. We explain this correspondence using the recent results on the equivalence of the…
The class of quantum affinizations includes quantum affine algebras and quantum toroidal algebras. In general they have no Hopf algebra structure, but have a "coproduct" (the Drinfeld coproduct) which does not produce tensor products of…
This work identifies the Reshetikhin-Turaev invariant of links in terms of a trace map on factorization homology. In particular, to recover the knot invariants associated to Chern-Simons theories, we construct a filtered…
We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological…
We describe the structure of the Whittaker or Gelfand-Graev module on a $n$-fold metaplectic cover of a $p$-adic group $G$ at both the Iwahori and spherical level. We express our answer in terms of the representation theory of a quantum…