Related papers: Additive Combinatorics Using Equivariant Cohomolog…
We explain how the approach of Andre and Quillen to defining cohomology and homology as suitable derived functors extends to generalized (co)homology theories, and how this identification may be used to study the relationship between them.…
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential…
The quantum cohomology of Grassmannians exhibits two symmetries related to the quantum product, namely a \Bbb {Z}/n action and an involution related to complex conjugation. We construct a new ring by dividing out these symmetries in an…
Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…
We give applications of equivariant Gromov--Hausdorff convergence in various contexts. Namely, using equivariant Gromov--Hausdorff convergence, we prove a stability result in the setting of compact finite dimensional Alexandrov spaces.…
An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…
This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…
This paper generalizes a result of Lynn on the "degree" of an equivariant cohomology ring $H^*_G(X)$. The degree of a graded module is a certain coefficient of its Poincar\'{e} series, and is closely related to multiplicity. In the present…
A generalisation of the equivariant Dixmier-Douady invariant is constructed as a second-degree cohomology class within a new semi-equivariant \v{C}ech cohomology theory. This invariant obstructs liftings of semi-equivariant principal…
We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both [Haglund 2004] and [Aval et al. 2014]. This settles in particular the cases…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which…
We define an equivariant $K_0$-theory for \textit{Yetter-Drinfeld} algebras over a Hopf algebra with an invertible antipode. We then show that this definition can be generalized to all Hopf-module algebras. We show that there exists a…
This paper investigates several classical and novel variations of the Erd\H{o}s--Szekeres problem, including multicolored point sets, convex hexagons with a given number of interior points, and polygons with constraints on edge colors. We…
For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the representation z^n is the cohomology of…
The paper presents a proof of the Hodge Riemann relations for the combinatorial intersection cohomology of a polytope, as fist given by K.Karu, in terms of geometric operations on polytopes.
This paper investigates the Erd\H{o}s distinct subset sums problem in $\mathbb{Z}^k$. Beyond the classical variance method, using alternative statistical quantities like $\mathbb{E}[\|X\|_1]$ and $\mathbb{E}[\|X\|_3^3]$ can yield better…
We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of…
The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools…
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…