Related papers: Equivariant geometric bordism, representation, lab…

Existing mathematical results are applied to the problem of classifying closed $p$-forms which are locally constructed from Lorentzian metrics on an $n$-dimensional orientable manifold $M$ ($0<p<n$). We show that the only closed, non-exact…

Recent work has applied scissors congruence $K$-theory to study classical cut-and-paste ($SK$) invariants of manifolds. This paper proves the conjecture that the squares $K$-theory of equivariant $SK$-manifolds arises as the fixed points of…

We define a GL-variety to be a (typically infinite dimensional) algebraic variety equipped with an action of the infinite general linear group under which the coordinate ring forms a polynomial representation. Such varieties have been used…

We identify the equivariant coinvariant ring of a pseudo-reflection group with its image under the localization map. We then show that this image can be realized as the equivariant cohomology of a sort linear hypergraph, analogous to a GKM…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb Z[a_1,a_2,\dots]$, ${\rm deg}(a_i)=2i$. In this paper we solve a…

In [Wyser-Yong '13] we introduced polynomial representatives of cohomology classes of orbit closures in the flag variety, for the symmetric pair $(GL_{p+q}, GL_p \times GL_q)$. We present analogous results for the remaining symmetric pairs…

In this paper we compute homotopical bordism rings $MU^G_*$ for abelian compact Lie groups G, giving explicit generators and relations. The key constructions are operations on equivariant bordism which should play an important role in…

Convex quadratically constrained quadratic programs (QCQPs) involve finding a solution within a convex feasible region defined by quadratic constraints while minimizing a convex quadratic objective function. These problems arise in various…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

The k-fold Cartesian product of a graph G is defined as a graph on k-tuples of vertices, where two tuples are connected if they form an edge in one of the positions and are equal in the rest. Starting with G as a single edge gives G^k as a…

Recently the first named author defined a 2-parametric family of groups $G_n^k$. Those groups may be regarded as analogues of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems led to the discovery of the…

We introduce and study a new class of topological $G$-spaces generalizing the classical flag manifolds $G/T$ of compact connected Lie groups. These spaces, which we call the $m$-quasi-flag manifolds $ F_m = F_m(G,T) $, are topological…

Let $G$ be a finite group, $X$ be a compact $G$-space. In this note we study the $(\mathbb{Z}_ + \times\mathbb{Z}/2\mathbb{Z})$-graded algebra $$\mathcal{F}^q_G(X) = \bigoplus_{n\geq0} q^n \cdot…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type corresponding to the…

We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results…

The Heilmann-Lieb Theorem on (univariate) matching polynomials states that the polynomial $\sum_k m_k(G) y^k$ has only real nonpositive zeros, in which $m_k(G)$ is the number of $k$-edge matchings of a graph $G$. There is a stronger…

Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V),…

We study the representation theory of the nested instantons quiver presented in [1], which describes a particular class of surface defects in four-dimensional supersymmetric gauge theories. We show that the moduli space of its stable…

$G$-equivariant convolutional neural networks (GCNNs) is a geometric deep learning model for data defined on a homogeneous $G$-space $\mathcal{M}$. GCNNs are designed to respect the global symmetry in $\mathcal{M}$, thereby facilitating…