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Binary stars play a critical role in determining both the dynamical evolution and the observational appearance of globular star clusters. We present a summary of three talks presented at IAU JD15, reviewing the current observational and…
The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those…
For a few pairs $G\subset \hat G$ of reductive groups, we study the decomposition of irreducible $\hait G$-modules into $G$-modules. In particular, we observe the saturation property for all of these pairs.
The idea of pairwise paracompactness was studied by many authors in a bitopological space. Here we study the same in the setting of more general structure of a bispace using the thoughts of the same given by Bose et al[2].
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. Here we study the onset of instability for an Earth-type planet that is…
Actions of a locally compact group G on a measure space X give rise to unitary representations of G on Hilbert spaces. We review results on the rigidity of these actions from the spectral point of view, that is, results about the existence…
Binaries are excellent astrophysical laboratories that provide us with direct measurements of fundamental stellar parameters. Compared to single isolated star, multiplicity induces new processes, offering the opportunity to confront our…
In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…
We show that if a nonscalar operator on a separable Hilbert space has a nontrivial invariant subspace, then it has also a nontrivial hyperinvariant subspace. Thus the hyperinvariant subspace problem is equivalent to the invariant subspace…
We describe the J-invariant of a semi-simple algebraic group G over a generic splitting field of a Tits algebra of G in terms of the J-invariant over a base field.
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite dimensional vector space $E$. B. Malgrange has shown that the space $\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant functions is a finite…
We analyze the observed distribution of the orbital eccentricity and period of binary radio pulsars in globular clusters using computational tools to simulate binary-single star interactions. Globular clusters have different groups of…
We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…
We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ over an algebraically closed field and $D$ is a divisor on $X$…
Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic…
We study some natural generalizations of the spectral spaces in the contexts of commutative rings and distributive lattices. We obtain a topological characterization for the spectra of commutative (not necessarily unitary) rings and we find…
We study intersections of orbits in polynomial semigroup dynamics with lines on the affine plane over a number field, extending previous work of D. Ghioca, T. Tucker, M. Zieve (2008)
In this paper we study the realizability question for commuting graphs of finite groups: Given an undirected graph $X$ is it the commuting graph of a group $G$? And if so, to determine such a group. We seek efficient algorithms for this…
We investigate orbit spaces of isometric actions on unit spheres and find a universal upper bound for the infimum of their curvatures.