Related papers: Rational curves on Grassmannians: systems theory, …

Let the vector bundle $\mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $\mathcal{E}$, also known as the polymology. This is…

In the present work the problem of distinguishing between essential and spurious (i.e., absorbable) constants contained in a metric tensor field in a Riemannian geometry is considered. The contribution of the study is the presentation of a…

In this survey we discuss the problem of the existence of rational curves on complex surfaces, both in the K\"ahler and non-K\"ahler setup. We systematically go through the Enriques--Kodaira classification of complex surfaces to highlight…

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…

For differential calculi over certain right coideal subalgebras of quantum groups the notion of quantum tangent space is introduced. In generalization of a result by Woronowicz a one to one correspondence between quantum tangent spaces and…

Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described…

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.

We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…

The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…

We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the…

Quantum Darwinism explains the emergence of classical reality from the underlying quantum reality by the fact that a quantum system is observed indirectly, by looking at parts of its environment, so that only specific information about the…

We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann's axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian…

Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present…

The ``generic'' family of classical sequential growth dynamics for causal sets provides cosmological models of causal sets which are a testing ground for ideas about the, as yet unknown, quantum theory. In particular we can investigate how…

Given a covering of the projective line with ramifications defined over a number field, we define a plain model of the algebraic curve realizing the Riemann existence theorem for this covering, and bound explicitly the defining equation of…

We argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This…

We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…

By directly probing the initial conditions of our universe, cosmological surveys offer us a unique observational handle on quantum field theory in curved spacetime with dynamical gravity and might even allow us to glean information about a…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…