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Here we propose BC$_3$, a graphene derivative that has been synthesized, as a platform to realize exotic quantum phases by introducing a moir\'e pattern with mismatched stacking. In twisted bilayer BC$_3$, it is shown that a crossover from…

We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality for N=1 theories with toric moduli spaces. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our…

We introduce, for a symmetric fusion category $\mathcal{A}$ with Drinfeld centre $\mathcal{Z}(\mathcal{A})$, the notion of $\mathcal{Z}(\mathcal{A})$-crossed braided tensor category. These are categories that are enriched over…

We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to…

Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…

Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the…

Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. They are a class of algebras with triangular decomposition, arising from a deformation problem, the…

Let $k$ be an algebraically closed field, $G$ a linear algebraic group over $k$ and $\varphi\in Aut(G)$, the group of all algebraic group automorphisms of $G$. Two elements $x, y$ of $G$ are said to be $\varphi$-twisted conjugate if…

Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of…

We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in…

We demonstrate how a 3-manifold, a Heegaard diagram, and a group presentation can each be interpreted as a pair of signed permutations in the symmetric group $S_d.$ We demonstrate the power of permutation data in programming and discuss an…

The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a…

A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…

Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which…

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

For every absolutely irreducible orthogonal representation of a twisted form of SL2 over a field of characteristic zero, we compute the "unique" symmetric bilinear form that is invariant under the group action. We also prove the analogous…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

For a tensor product of algebras twisted by a bicharacter, we completely describe its Hochschild cohomology, as a Gerstenhaber algebra, in terms of the Hochschild cohomology of its component parts. This description generalizes a result of…

In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.

Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(Z), and to a 3-manifold Y with boundary, together with an orientation-preserving diffeomorphism \phi from F to \bdy Y, a module…