Related papers: Real monodromy action
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…
In this talk, we show how the monodromy matrix, ${\hat{\cal M}}$, can be constructed for the two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
Two parameter families of plane conics are called nets of conics. There is a natural group action on the vector space of nets of conics, namely the product of the group reparametrizing the underlying plane, and the group reparametrizing the…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
Based mainly on examples of interest in mechanics, we define the notion of a polite group action. One may view this as not only trying to give a more general notion than properness of a group action, but also to more fully understand the…
In the spirit of the action of the symmetric group on the ring of polynomials in $n$ variables, we consider the actions of the seven frieze groups on rings of formal infinite linear combinations of monomials of restricted degree. For each…
The theory of iterated monodromy groups was developed by Nekrashevych. It is a wonderful example of application of group theory in dynamical systems and, in particular, in holomorphic dynamics. Iterated monodromy groups encode in a…
Various spaces of symmetries of a structure are naturally endowed with both an algebraic and a topological structure. For example, the automorphism group of a structure is, on top of being a group, a topological group when equipped with the…
We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…
Let X be a smooth separated geometrically connected variety over F_q and f:Y-> X a smooth projective morphism. We compare the invariant dimensions of the l-adic representation V_l and the F_l-representation \bar V_l of the geometric \'etale…
Though algebraic geometry over $\mathbb C$ is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the $n\times n\times n$…
We study equivariant morphisms from zero dimensional schemes to varieties and show that, under suitable assumptions, all such morphisms factor via a canonical one. We relate the above to Algebraic Representations of Ergodic Actions.
For an ample line bundle $\mathcal{L}$ on a complete toric surface $X$, we consider the subset $V_{\mathcal{L}} \subset \vert \mathcal{L} \vert$ of irreducible, nodal, rational curves contained in the smooth locus of $X$. We study the…
The real type of a finite family of univariate polynomials characterizes the combined sign behavior of the polynomials over the real line. We derive an explicit formula for the number of real types subject to given degree bounds. For the…
We study the existence and left properness of transferred model structures for "monoid-like" objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular,…
We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson bracket relations of the model contain derivatives, this computation leads to a peculiar type of symmetry breaking which…
Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we…
We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the…