Related papers: The Sullivan dictionary and Bowen-Series maps
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge…
We prove an analogue of the Manin-Mumford conjecture for polynomial dynamical systems over number fields. In our setting the role of torsion points is taken by the small orbit of a point $\alpha$. The small orbit of a point was introduced…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…
We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting,…
These are lectures on discrete groups of isometries of complex hyperbolic spaces, aimed to discuss interactions between the function theory on complex hyperbolic manifolds and the theory of discrete groups.
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
We compute relations of rational equivalence among special codimensional two cycles on families of abelian surfaces using elements of higher chow groups.
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components -…
We describe the spaces of stability conditions on certain triangulated categories associated to Dynkin diagrams. These categories can be defined either algebraically via module categories of preprojective algebras, or geometrically via…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…
We interpret the chiral WZNW model with general monodromy as an infinite dimensional quasi-Hamiltonian dynamical system. This interpretation permits to explain the totality of complicated cross-terms in the symplectic structures of various…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…
These notes contain a brief introduction to rational homotopy theory: its model category foundations, the Sullivan model and interactions with the theory of local commutative rings.
A class of simple filtered Lie algebras of polynomial growth with increasing filtration is distinguished and presentations of these algebras are explicitely described for the simplest examples. Lie (super)algebras of this class appear in…