Related papers: Lectures on Orientifolds and Duality
This is a tutorial on duality properties of special functions, mainly of orthogonal polynomials in the ($q$-)Askey scheme. It is based on the first part of the 2017 R.P. Agarwal Memorial Lecture delivered by the author.
Exact duality in supersymmetric gauge theories leads to highly non-trivial predictions about the moduli spaces of BPS monopole solutions. These notes attempt to be a pedagogical review of the current status of these investigations and are…
This contribution to the XXVII Symposium on Multiparticle Dynamics held in Frascati, Italy, September, 1997 consists of the following subject matter: (1) Introductory generalities. (2) Brief mention of some of the contributions to the…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
These notes overlap with lectures given at the TASI summer schools in 2014 and 2011, as well as at the European School of High Energy Physics in 2013. This is primarily an attempt at transcribing my hand-written notes, with emphasis on…
Modern cosmology poses deep and unavoidable questions for fundamental physics. In this plenary talk, delivered in slightly different forms at the {\it Particles and Nuclei International Conference} (PANIC05) in Santa Fe, in October 2005,…
These lecture notes are based on three lectures, each ninety minutes long, given by the author at the "International School on Strings and Fundamental Physics" which took place in Garching/Munich from July 25 to August 6, 2010. These…
Late Winter Lecture Notes, Short Course (10 hours) of Relativistic Astrophysics held at the Department of Physics and Astronomy of the University of Padova, March 13-17, 2017. Third version.
The International School on Cosmological Dark Matter held in Valencia in the fall of 1993 was devoted to the interplay of cosmology and particle physics, with the obvious emphasis on the Dark Matter issue. Here I present the expanded…
These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of…
These four lectures, given at the British Universities Summer School in Theoretical Elementary Particle Physics (BUSSTEPP), held in 2014 in Southampton, are a brief introduction to a selection of current topics in physics Beyond the…
These are extended lecture notes of a PhD course that the author gave at the Universita degli studi di Torino in Italy in spring 2013.
The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of…
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…
These are lecture notes of the Summer school on the geometry of differential equations held in Nordfjordeid, Norway in 1996. They cover geometric structures related to scalar second order ODEs, the construction of the associated Cartan…
The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional…
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.
The duality cascade, and its dual description as string theory on the warped deformed conifold, brings together several sophisticated topics, some of which are not widely known. These lectures, which contain a number of previously…
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.