Related papers: Singularities of inverse functions
We formulate a resolution of singularities algorithm for analyzing the zero sets of real-analytic functions in dimensions $\geq 3$. Rather than using the celebrated result of Hironaka, the algorithm is modeled on a more explicit and…
This is an expanded set of notes based on two lectures given by the author at the 2022 IHES summer school on the Langlands program, on explicit techniques for the construction of automorphic representations.
The local multiplicities of the Maxwell sets in the spaces of versal deformations of Pham holomorphic function singularities are calculated. A similar calculation for some other bifurcation sets (generalized Stokes' sets) defined by more…
We prove identities between cycle integrals of non-holomorphic modular forms arising from applications of various differential operators to weak Maass forms.
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…
This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…
The purpose of this is the study of certain coherent sheaves of meromorphic forms on reduced complex space and particularly their behavior with respect to pull back and higher direct image.
This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan…
This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…
We study the inverse Langevin function $\mathscr{L}^{-1}(x)$ because of its importance in modelling limited-stretch elasticity where the stress and strain energy become infinite as a certain maximum strain is approached, modelled here by…
A summary of the recent experimental, phenomenological and theoretical results presented in the Structure Functions working group at DIS2012 workshop.
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
The article provides a local classification of singularities of meromorphic second order linear differential equation with respect to analytic/meromorphic linear point transformations. It also addresses the problem of determining the Lie…
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…
We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…
We construct a (non K\"ahler) compact complex 3-dimensional manifold $X$ having two following properties: 1) for any domain $D$ in $C^2$ every meromorphic map $f$ from this domain into $X$ extends to a meromorphic map from the envelope of…
In this series of lectures, I will discuss results for complex hypersurfaces with non-isolated singularities. In Lecture 1, I will review basic definitions and results on complex hypersurfaces, and then present classical material on the…
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…