Related papers: Lecture notes on torsions
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
Lecture notes on quantum machine learning for computer scientists.
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
This is the first version of a submission made to vixra back in August 2009. It is concerned with the exploration of various ideas due to Roy Frieden of the University of Arizona in his manuscript "Physics from Fisher Information", which…
Expository notes on the Schwarz lemma born out of some lectures given on the subject.
The Ray-Singer analytic torsion is the zeta-function trace of a certain sum of logarithm operators on the de Rham complex. In this note we examine the residue analytic torsion, defined using the residue-trace instead of the spectral zeta…
These are the notes for my 2017 Takagi lectures on DT counts of curves in algebraic threefolds. We discuss the fundamentals of the subject, its origins, open questions, and certain recent advances.
This is a short arrangement of notes on D-branes, offered as an embellishment of five lectures which were presented at the 1998 Trieste Spring School entitled ``Non-Perturbative Aspects of String Theory and Supersymmetric Gauge Theory''.…
Introductory lectures on SCET mainly following the first chapters of arXiv:1410.1892
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes…
In these lecture notes I describe the theory of QCD and its application, through perturbation theory, at particle colliders.
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews…
We study the Reidemeister torsion and the analytic torsion of the $m$ dimensional disc in the Euclidean $m$ dimensional space, using the base for the homology defined by Ray and Singer in \cite{RS}. We prove that the Reidemeister torsion…
Informal lecture notes with examples on sheaf theory and the derived category of sheaves; sheaves and Morse theory; perverse sheaves, and some applications to representation theory. Added Oct 2021: cellular perverse sheaves. Proofs are…
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
An overview is given of the application of twistor geometric ideas to supersymmetry with particular emphasis on the construction of superspaces associated with four-dimensional spacetime. Talk given at Leuven conference, July 1995.
This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…