Related papers: All what I wanted to know about Langlands program …
In experimental physics, lab notebooks play an essential role in the research process. For all of the ubiquity of lab notebooks, little formal attention has been paid to addressing what is considered `best practice' for scientific…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
Preregistration refers to the practice of specifying what you are going to do, and what you expect to find in your study, before carrying out the study. This practice is increasingly common in medicine and psychology, but is rarely…
We present topics in the Langlands Program to graduate students and a wider mathematically mature audience. We study both global and local aspects in characteristic zero as well as characteristic $p$. We look at modern approaches to the…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
These notes give a statement of the "fundamental lemma," which is a conjectural identity between p-adic integrals that arises as part of the Langlands program.
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
The primary aim of this paper is to suggest questions for future discourse and research of specialized programming courses in the Humanities. Specifically I ask whether specialized courses promote the production of fragile programming…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
This is a credit mini-course in French prepared for a Summer School at the University of Sherbrooke. The course consists of three one-and-half hour lectures and three credit exercises for a class of advanced graduate students.
This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book "The Genesis of Langlands' Program," edited by Dr. Julia Mueller and Dr. Freydoon…
My notes on Deep Learning for NLP.
Computer programs are part of our daily life, we use them, we provide them with data, they support our decisions, they help us remember, they control machines, etc. Programs are made by people, but in most cases we are not their authors, so…
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.
The purpose of this paper is to survey some of the important results on Langlands program, global fields, $D$-shtukas and finite shtukas which have influenced the development of algebra and number theory. It is intended to be selective…
This is a survey lecture note on the applications of Langlands functoriality which were obtained recently by some people at the Langalnds school. This lecture was delivered at the Department of Mathematics, Kyoto University, Japan on June…
These notes are based on lectures given in Wuhan (China) in July 2007. Their aim is to provide an introduction to Langlands philosophy.
These are the notes from my courses on the arithmetic of quadratic forms.
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…