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Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on…
We describe transposed Poisson structures on the upper triangular matrix Lie algebra $T_n(F)$, $n>1$, over a field $F$ of characteristic zero. We prove that, for $n>2$, any such structure is either of Poisson type or the orthogonal sum of a…
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…
The nonelliptic $\mathsf{A_2}$-webs with $k$ "$+$"s on the top boundary and $3n-2k$ "$-$"s on the bottom boundary combinatorially model the space $\mathsf{Hom}_{\mathfrak{sl}_3}(\mathsf{V}^{\otimes (3n-2k)}, \mathsf{V}^{\otimes k})$ of…
We prove that the restriction of Bruhat order to noncrossing partitions in type $A_n$ for the Coxeter element $c=s_1s_2 ...s_n$ forms a distributive lattice isomorphic to the order ideals of the root poset ordered by inclusion. Motivated by…
As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the…
The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A…
Fulton and Kraskiewicz gave a presentation of Specht modules as a quotient of the space of column tabloids by dual Garnir relations. We simplify this presentation by showing that it can be generated by a single relation for each pair of…
A $\mathrm{U}(p,q)$-Higgs bundle on a Riemann surface (twisted by a line bundle) consists of a pair of holomorphic vector bundles, together with a pair of (twisted) maps between them. Their moduli spaces depend on a real parameter $\alpha$.…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
We examine the cell modules for the category of type An webs and their natural cellular forms. We modify the bases of these modules, as described by Elias, to obtain an orthogonal basis of each cell module. Hence, we calculate the…
We study a generalization of the partially asymmetric exclusion process (PASEP) in which there are $k$ species of particles of varying weights hopping right and left on a one-dimensional lattice of $n$ sites with open boundaries. In this…
A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.
We introduce a lifting of West's stack-sorting map $s$ to partition diagrams, which are combinatorial objects indexing bases of partition algebras. Our lifting $\mathscr{S}$ of $s$ is such that $\mathscr{S}$ behaves in the same way as $s$…
The combinatorics of certain osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. More specifically, the paths being considered have fixed start and end points on respectively the lower and right…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
The descent-to-peak map serves as a bridge between algebra and combinatorics. We use it as a tool for proving the equidistribution of peak and valley sets of standard Young tableaux with a very short argument. We also introduce a new…
This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…