相关论文: The Eynard--Orantin recursion for simple singulari…

We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent…

We first review our previous work arxiv:1503.02993 [math-ph] where we considered a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco and showed that extending this Hopf Algebra by…

We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a…

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…

We study the commutants of a Schr\"{o}dinger operator whose potential function possesses inverse square singularities along some hyperplanes passing through the origin. It is shown that the Weyl group symmetry of the potential function and…

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…

Given a normal surface singularity (X,0), its link, M is a closed differentiable three dimensional manifold which carries much analytic information. It is an interesting question to ask whether, under suitable analytic and topological…

We study the behavior of spatially homogeneous brane-worlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these brane-worlds can be locally either isotropic or…

The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main…

The local invariants of a meromorphic quadratic differential on a compact Riemann surface are the orders of zeros and poles, and the residues at the poles of even orders. The main result of this paper is that with few exceptions, every…

Ordinary maps satisfy topological recursion for a certain spectral curve $(x, y)$. We solve a conjecture from arXiv:1710.07851 that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy…

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…

We consider a natural generalisation of the Painlev\'e property and use it to identify the known integrable cases of the Lane-Emden equation with a real positive index. We classify certain first-order ordinary differential equations with…

We state a version of the crepant resolution conjecture for total ancestor potentials for surface singularities, and reduce the conjecture to the quantum McKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishing conjecture…

In the study of equisingularity of isolated singularities we have the classical theorem of Briancon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the…

We evaluate the propagator of scalar and spinor in three dimensional quantum electrodynamics with the use of Ward-Identity for soft-photon emission vertex.We work well in position space to treat infrared divergences in our model.…

The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…

In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal…

For any vector bundle, we define an inverse system of spectra. In the case of a trivial bundle over a point, the homotopy groups of the filtration quotients give rise to the stable EHP spectral sequence, as was shown by Mahowald. The limit…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…