Related papers: A few problems on monodromy and discriminants
We study a class of $p$-Laplacian Dirichlet problems with weights that are possibly singular on the boundary of the domain, and obtain nontrivial solutions using Morse theory. In the absence of a direct sum decomposition, we use a…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.
A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence…
We study movable singularities of Garnier systems using the connection of the latter with isomonodromic deformations of Fuchsian systems. Questions on the existence of solutions for some inverse monodromy problems are also considered.
We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem-Mahler-Lech theorem to rational function…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
We consider the variety of $(p+1)$-tuples of matrices $M_j$ from given conjugacy classes from $GL(n,{\bf C})$ such that $M_1... M_{p+1}=I$. This variety is connected with the Deligne-Simpson problem and the matrices $M_j$ are interpreted as…
mu-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms…
We consider the monodromy at infinity and the monodromies around the bifurcation points of polynomial functions $f : \CC^n \longrightarrow \CC$ which are not tame and might have non-isolated singularities. Our description of their Jordan…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of C^m into P^n with truncated multiplicities and "few" targets. We also give a theorem of linear degeneration for such maps…
We introduce a novel monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. This problem is prevalent in…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
The number of Morse points in a Morsification determines the topology of the Milnor fibre of a holomorphic function germ $f$ with isolated singularity. If $f$ has an arbitrary singular locus, then this nice relation to the Milnor fibre…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.
We present an account of different problems that arise in relation with cyclicity problems in Dirichlet-type spaces, in particular with polynomials $p$ that minimize the norm $\|pf-1\|$.
This article surveys recent advances and future challenges in the $2$-representation theory of finitary $2$-categories with a particular emphasis on problems related to classification of various classes of $2$-representations.
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP-complete. Thus while…