Related papers: A path model for MV polytopes in type A_n

Given a positive function F on Sn which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas…

An $S$-hypersimplex for $S \subseteq \{0,1, \dots,d\}$ is the convex hull of all $0/1$-vectors of length $d$ with coordinate sum in $S$. These polytopes generalize the classical hypersimplices as well as cubes, crosspolytopes, and…

This paper establishes compactness results for the moduli stack of holomorphic curves in suitable exploded manifolds. This result together with the analysis in arXiv:0902.0087 allows the definition of Gromov Witten invariants of these…

Let $H$ be a Hopf algebra with a modular pair in involution $(\Character,1)$. Let $A$ be a (module) algebra over $H$ equipped with a non-degenerated $\Character$-invariant $1$-trace $\tau$. We show that Connes-Moscovici characteristic map…

In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…

We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$-gon with a small disk in the centre. This model provides convenient and uniform interpretations for…

This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…

One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic…

We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion…

In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the…

In this paper we obtain a system of flat coordinates on the monodromy manifold of each of the Painlev\'e equations. This allows us to quantise such manifolds. We produce a quantum confluence procedure between cubics in such a way that…

We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…

A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov Theorem, any such curve admits a definite symmetric determinantal representation. We use polynomial homotopy continuation to…

We show that Witt groups of spinor varieties (aka.\ maximal isotropic Grassmannians) can be presented by combinatorial objects called even shifted young diagram. Our method relies on the Blow-up setup of Balmer-Calm\`es, and we investigate…

In 1999, Katona and Kierstead conjectured that if a $k$-uniform hypergraph $\cal H$ on $n$ vertices has minimum co-degree $\lfloor \frac{n-k+3}{2}\rfloor$, i.e., each set of $k-1$ vertices is contained in at least $\lfloor…

We prove the genus zero part of the generalized Witten conjecture relating moduli spaces of spin curves to Gelfand-Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a…

We introduce surface Minkowski tensors to characterize rotational symmetries of shapes embedded in curved surfaces. The definition is based on a modified vector transport of the shapes boundary co-normal into a reference point which…

Steenrod homotopy theory is a framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; from another viewpoint, it studies the topology of the lim^1 functor (for inverse sequences of groups). This…

We generalise Kahn, Miyazaki, Saito, Yamazaki's theory of modulus pairs to pairs $(X, D)$ consisting of a qcqs scheme $X$ equipped with an effective Cartier divisor $D$ representing a ramification bound. We develop theories of sheaves on…