相关论文: Notes on Free Probability Theory

This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an…

These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…

Wextend the results obtained recently by G. D'Ambra and A. Loi towards the proof of a conjecture of M.Gromov on isometric immersions via non-free maps.

Concluding talk, Physics at LHC 2004, Vienna

This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting theorems (CLT, CCLT, PLT, CPLT), and with a look into examples…

Preliminary version No.~2 of the lecture notes for the talk ``Quantum theory of gravitational collapse'' given at the 271. WE-Heraeus-Seminar ``Aspects of Quantum Gravity'' at Bad Honnef, 25 February--1 March 2002

These are the (somewhat extended) lecture notes for four lectures delivered at the spring school during the thematic programme "Mathematical Perspectives of Gravitation beyond the Vacuum Regime" at ESI Vienna in February 2022.

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to…

These notes provide an introductory exposition of the Seiberg-Witten gauge theory. They collect the material presented in a series of seminars given by the author at the University of Milano.

A distance between von Neumann algebras is introduced, depending on a further norm inducing the $w^*$-topology on bounded sets. Such notion is related both with the Gromov-Hausdorff distance for quantum metric spaces of Rieffel and with the…

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

These lectures centered around the Kempf-Ness theorem, which describes the equivalence between notions of quotient in symplectic and algebraic geometry. The text also describes connections to invariant theory, such existence of invariants…

We describe the freedom of choosing a square root in massive gravity from algebraic point of view. This contribution is based on the talk given by one of us (AG) at the Geometric Foundations of Gravity conference in Tartu in August 2017.

This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…

The present review aims both to offer some motivations and mathematical prerequisites for a study of NCG from the viewpoint of a theoretical physicist and to show a few applications to matrix theory and results obtained. Lectures given by…

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

We begin herewith the editing of physics notes taken in the course of Journal Club seminars at INFN-LNF in 1996. The activity consists of informal talks about work in progress and/or review of (more or less) recent physics results of…

These are (not updated) notes from the lectures I gave in St.Petersburg in July of 2001. Their goal is to give an expository account of the proof of Kontsevich's combinatorial formula for intersections on moduli spaces of curves following…

This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institute of Mathematics, Nankai University, Tianjin, China. July…