Related papers: Lectures on the Strominger system
We construct a moduli space of formally integrable and involutive ideal sheaves arising from systems of partial differential equations (PDEs) in the algebro-geometric setting, by introducing the $\mathcal{D}$-Hilbert and $\mathcal{D}$-Quot…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications,…
We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian…
We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a…
This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry…
This preprint is the introduction of my habilitation thesis for Paris7 university. It is a sumary of a collection of works on the 2 matrix model. In an introduction, 3 different and unequivalent definitions of matrix models are given…
This paper solves the global moduli problem for regular holonomic D-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to…
This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture…
This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…
In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition…
This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging…
In these lectures I review the progress made over the last few years in the subject of string and string-inspired phenomenology. I take a practical approach, thereby concentrating more on explicit examples rather than on formal…
We systematically study Lorentz symmetry extensions in quantum field theories (QFTs) and their 't Hooft anomalies via cobordism. The total symmetry $G'$ can be expressed in terms of the extension of Lorentz symmetry $G_L$ by an internal…
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
We produce the general solution of the Wess-Zumino consistency condition for gauge theories of the Yang-mills type, for any ghost number and form degree. We resolve the problem of the cohomological independence of these solutions. In other…
These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild…
We present some results that complement our prequels [arXiv:1809.08425,arXiv:1907.05770] on holomorphic vector bundles. We apply the method of the Quot-scheme limit of Fubini-Study metrics developed therein to provide a generalisation to…
In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…