Related papers: The Noncommutative Infinitesimal Equivariant Index…

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kahler manifold. We use normalizations of the canonical trace density of a star product and of the…

We consider an equisingularity problem for polynomial families of affine hypersurfaces $X_\tau \subset \mathbb C^n$ with (at worst) isolated singularities. We show that the constancy of the global polar invariants $\gamma^* (X_\tau)$ is…

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.

In this paper, we define the quotinet graphs. In particular, we introduce the boundary quotient graphs, admissible boundary quotient graphs and subgraph boundary qoutient graphs. By the property of the quotient spaces, the boundary…

Let $T$ be a circle group, and $LT$ be its loop group. We hope to establish an index theory for infinite-dimensional manifolds which $LT$ acts on, including Hamiltonian $LT$-spaces, from the viewpoint of $KK$-theory. We have already…

The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…

We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…

For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to…

We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure $\mu$ on…

It is well known that very special $\Gamma$-spaces and grouplike $\E_\infty$ spaces both model connective spectra. Both these models have equivariant analogues. Shimakawa defined the category of equivariant $\Gamma$-spaces and showed that…

In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4-dimensional manifold, we compute this…

Exploiting symmetry in Groebner basis computations is difficult when the symmetry takes the form of a group acting by automorphisms on monomials in finitely many variables. This is largely due to the fact that the group elements, being…

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…

We introduce a family $\mathbb{M}_{r;f,\eta}$ of infinitesimal supergroup schemes, which we call multiparameter supergroups, that generalize the infinitesimal Frobenius kernels $\mathbb{G}_{a(r)}$ of the additive group scheme…

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and…

There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…

In this paper, we study properties of the heat semigroup of configuration space analysis. Using a natural ``Riemannian-like'' structure of the configuration space $\Gamma_X$ over a complete, connected, oriented, and stochastically complete…