Related papers: Desingularisation de metriques d'Einstein. II
We treat the problem of defining, and characterising in a practical way, an appropriate class of distinguished curves for Poincar\'e-Einstein manifolds, and other conformally singular geometries. These "generalised geodesics" agree with…
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue…
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…
We find new obstructions to the desingularization of compact Einstein orbifolds by smooth Einstein metrics. These new obstructions, specific to the compact situation, raise the question of whether a compact Einstein $4$-orbifold which is…
We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups {\Gamma}_0 (pq) with p and q distinct odd primes, giving an answer to a…
We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It…
Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.
The first paper of this series introduced objects (elements of twisted relative cohomology) that are Poincar\'e dual to Feynman integrals. We show how to use the pairing between these spaces -- an algebraic invariant called the intersection…
We describe a general procedure for computing renormalized curvature integrals on Poincar\'e-Einstein manifolds. In particular, we explain the connection between the Gauss-Bonnet-type formulas of Albin and Chang-Qing-Yang for the…
A growing body of evidence suggests that the complexity of Feynman integrals is best understood through geometry. Recent mathematical developments [Kontsevich and Soibelman, arXiv:2402.07343] have illuminated the role of exponential…
We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, valid for any theory with a 4d N=2 supergravity description. Our argument leads to a slight generalization of the formula, which relates monodromy…
A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed…
A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…
We present an explicit upper bound on the number of isolated homogeneous Einstein metrics on compact homogeneous spaces whose isotropy representations consist of pairwise inequivalent irreducibles. This is the BKK bound of the corresponding…
In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the…
We investigate the wall-crossing phenomena for moduli of framed quiver representations. These spaces are expected to be highly useful in capturing the representation theoretic essence of special functions in integrable systems. Within this…
We construct a family of split signature Einstein metrics in four dimensions, corresponding to particular classes of third order ODEs considered modulo fiber preserving transformations of variables.
Invariant Einstein metrics on generalized Wallach spaces have been classified except $SO(k+l+m)/SO(k)\times SO(l)\times SO(m)$. In this paper, we give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and…
In this paper, we extend the existence and regularity theorems for K\"ahler-Einstein metrics having conic singularities along a simple normal crossing divisor to the case of normal crossing divisor, i.e. when components of the divisor are…
We first provide an alternative proof of the classical Weitzneb\"ock formula for Einstein four-manifolds using Berger curvature decomposition, motivated by which we establish a unified framework for a Weitzenb\"ock formula for a large class…