Related papers: Equivariant spectral flow and a Lefschetz theorem …
The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…
We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in…
In [10], Dabrowski etc. gave spectral Einstein bilinear functionals of differential forms for the Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski…
We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are defined. These estimates are expressed in…
Given a bounded domain in the Euclidean space satisfying the uniform outer cone condition, we show that a uniformly elliptic operator of second order with continuous second order coefficients generates a holomorphic semigroup on the space…
Following Hausel-Hitchin, we investigate core Lagrangians and upward flows in Hilbert schemes of points on elliptic surfaces. We compute the scheme-theoretic multiplicities of core Lagrangians, as well as the equivariant multiplicities of…
We prove an equivariant Lefschetz formula for elliptic complexes over a compact manifold carrying the action of a compact Lie group of isometries via heat equation methods.
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
We introduce the notion of the joint spectral flow, which is a generalization of the spectral flow, by using Segal's model of the connective $K$-theory spectrum. We apply it for some localization results of indices motivated by Witten's…
An analytic definition of a $\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings…
In this paper, we consider incompressible Euler flows in $ \mathbb{R}^{4} $ under bi-rotational symmetry, namely solutions that are invariant under rotations in $\mathbb{R}^{4}$ fixing either the first two or last two axes. With the…
In this paper, we consider a Riemannian manifold (M, g) endowed with a Riemannian flow and we study the curvature term in the Bochner-Weitzenb{\"o}ck formula of the basic Laplacian on M. We prove that this term splits into two parts. The…
In this article, we continue the discussion of Fang-Wu (2015) to estimate the spectral gap of the Ornstein-Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along with explicit estimates we study the…
We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K_0 of the category of "phi-endomorphisms of finitely generated free…
The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the intersections of concrete families of elliptic operators with…
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold that is locally modeled on $R^n$ modulo the action of a finite group. Orbifolds have proven interesting in a variety of settings. Spectral geometers have…
There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup $U = {\begin{pmatrix} 1 & * 0 & 1 \end{pmatrix}}$. We classify the U-invariant ergodic measures on certain…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of…
We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…