Related papers: Whitney's index formula in higher dimensions and L…
We introduce and study the Weingarten calculus for centered random permutation matrices in the symmetric group S_N. After presenting a formulation of the Weingarten calculus on the symmetric group, we derive a formula in the centered case,…
Discrete series Whittaker functions on $Spin(2n, 2)$ are studied. The dimensions of the space of both algebraic and continuous Whittaker models are explicitly determined. They are described by a sum of dimensions of irreducible…
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically,…
We describe the Stiefel-Whitney classes (SWCs) of orthogonal representations $\pi$ of the finite special linear groups $G=\text{SL}(2,\mathbb F_q)$, in terms of character values of $\pi$. From this calculation, we can answer interesting…
We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of…
We determine the number of singularities - counted whit multiplicities - of generic distributions of dimension and codimension one on smooth complete intersections in compact toric orbifolds with isolated singularities. We also present some…
The factorisation of scattering amplitude is described by the Weinberg theorem. In this talk, we will show the universality of the theorem at the next leading correction of the soft expansion. For that we will derive the soft operator by…
We express nested Hilbert schemes of points and curves on a smooth projective surface as "virtual resolutions" of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories…
We prove a simultaneous generalization of the classical Riemann-Hurwitz and Plucker formulas, addressing the total inflection of a morphism from a (smooth, projective) curve to an arbitrary (smooth, projective) higher-dimensional variety.…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
We show that certain structures and constructions of the Whitham theory, an essential part of the perturbation theory of soliton equations, can be instrumental in understanding the geometry of the moduli spaces of Riemann surfaces with…
This article treats the Picard group of the moduli (stack) of r-spin curves and its compactification. Generalized spin curves, or r-spin curves are a natural generalization of 2-spin curves (algebraic curves with a theta-characteristic),…
We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual \v{C}ech filtration of such a subset can be endowed with a vector…
We prove a Tracy-Widom type formula for the generating function of occupancy numbers on several disjoint intervals of the higher order Airy point processes. The formula is related to a new vector-valued Painlev\'e II hierarchy we define,…
The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold…
We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed…
Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…
The goal of this note is to define biparametric persistence diagrams for smooth generic mappings $h=(f,g):M\to V\cong \mathbb{R}^2$ for smooth compact manifold $M$. Existing approaches to multivariate persistence are mostly centered on the…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
We formulate Witten index problems for theories with two supercharges in a Majorana doublet, as in $d=3$ $\mathcal N=1$ theories and dimensional reduction thereof. Regardless of spacetime dimensions, the wall-crossing occurs generically, in…