Related papers: Monodromy at infinity of $A$-hypergeometric functi…

In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…

We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization…

We present a moduli space for all hyperbolic basic sets of diffeomorphisms on surfaces that have an invariant measure that is absolutely continuous with respect to Hausdorff measure. To do this we introduce two new invariants: the measure…

The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with infinite number of variables. We adopt von Koch and Hilbert's definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type…

Given any connected topological space $X$, assume that there exists an epimorphism $\phi: \pi_1(X) \to \mathbb{Z}$. The deck transformation group $\mathbb{Z}$ acts on the associated infinite cyclic cover $X^\phi$ of $X$, hence on the…

We study multivariate Mellin transforms of Laurent polynomials by considering special toric compactifications which make their singular structure apparent. This gives a precise description of their convergence domain, refining results of…

We discuss the history of the monodromy theorem, starting from Weierstra\ss, and the concept of monodromy group. From this viewpoint we compare then the Weierstra\ss , the Legendre and other normal forms for elliptic curves, explaining…

We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous representative of such a function has a pointwise limit at…

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…

We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

The main theorem of this paper asserts that the inclusion of the space of projective Lagrangian planes into the space of Lagrangian submanifolds of complex projective space induces an injective homomorphism of fundamental groups. We…

Let $(M,g)$ be a two-dimensional compact boundaryless Riemannian manifold with nonpostive curvature, then we shall give improved estimates for the $L^2$-norms of the restrictions of eigenfunctions to unit-length geodesics, compared to the…

Let $A$ be an infinite Toeplitz matrix with a real symbol $f$ defined on $[-\pi, \pi]$. It is well known that the sequence of spectra of finite truncations $A_N$ of $A$ converges to the convex hull of the range of $f$. Recently, Levitin and…

We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as…

In this paper, we show that the generalized hypergeometric function mF_m-1 has a one parameter group of local symmetries, which is a conjugation of a flow of a rational Calogero-Mozer system. We use the symmetry to construct fermionic…

We prove that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures. The set of ergodic measures of these pseudo-rotations consists of the measure induced by the…

We investigate the structure of logarithmic modes in critical topologically massive gravity (CTMG) at the chiral point $\mu \ell=1$ from the perspective of analytic continuation and monodromy. Starting from the degeneration of massive and…

We construct some families of automorphic forms on Grassmannians which have singularities along smaller sub Grassmannians, using Harvey and Moore's extension of the Howe (or theta) correspondence to modular forms with poles at cusps. Some…

The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…