Related papers: Notes on transformations in integrable geometry
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
We discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, like the Gauss/Bonnet theorem and the mean-curvature force…
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
In this series of lectures, we (re)view the "geometric method" that reconstructs, from a geometric object: the "spectral curve", an integrable system, and in particular its Tau function, Baker-Akhiezer functions and "current amplitudes",…
We present a thorough analysis on the invariance of the most widely used metrics in the Geometrothermodynamics (GTD) programme. We centre our attention in the invariance of the curvature of the space of equilibrium states under a change of…
The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical…
The fidelity per site between two ground states of a quantum lattice system corresponding to different values of the control parameter defines a surface embedded in a Euclidean space. The Gaussian curvature naturally quantifies quantum…
This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic…
We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to…
We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.
Gauging a symmetry can be thought of as the insertion of a spacetime-filling defect. Accordingly, we regard each gaugeable symmetry in a theory as defining a $-1$-form symmetry via condensation. The resulting operators, called gauge…
This is a corrected version of my paper "Application of integral geometry to minimal surfaces" appeared in International J. Math. vol. 4 Nr. 1 (1993), 89-111. The correction concerns Proposition 3.5. We discuss this correction in Appendix…
A general method for analytic inversion of geometric integral transforms is proposed
The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with…
This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link…