Related papers: Combinatorial and Additive Number Theory Problem S…
This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was…
Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
In this conference proceedings, some comments on the present status and recent growth of efforts to find Lorentz and CPT violation are given by extracting metrics from the annually updated "Data Tables for Lorentz and CPT Violation." They…
We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples. The major…
This paper presents results of topic modeling and network models of topics using the International Conference on Computational Science corpus, which contains domain-specific (computational science) papers over sixteen years (a total of 5695…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same authors (along with Spielman) which appeared at the 2014 ICM. In…
We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An earlier version of this chapter (originally Chapter 5) has been available on the course website since…
These are notes for the course CS-172 I first taught in the Fall 1986 at UC Berkeley and subsequently at Boston University. The goal was to introduce the undergraduates to basic concepts of Theory of Computation and to provoke their…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive…
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…
These are ten lectures on the moment problem delivered by the author at the Vietnam Institute of Advanced Studies in Mathematics, Hanoi, March 2019. The first 3 lectures are about the one-dimensional full and truncated moment problem. The…