Related papers: Some aspects of explicit birational geometry inspi…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable…

First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th…

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…

This survey is an invitation to recent developments in higher dimensional birational geometry.

We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…

The relevance of the algebraic entropy in the study of birational discrete time dynamical systems highlights the need to relate it to other characteristics of these systems. In this letter, two complementary proofs are given that the…

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…

In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…

We study the automorphisms of compact K\"ahler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that…

These lecture notes are written for a PhD mini-course I gave at the CIRM in Luminy in 2019. Their intended purpose was to present, in the context of smooth toric varieties, a relatively self-contained and elementary introduction to the…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

We give an account of old and new results concerning many types of non-K\"ahler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behaviour at deformations and blow-up. We also describe a…

We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.

We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is…

This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…

The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…

We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…