Speaker affiliation: Henry Ford II Professor of Statistics and Data Science, Yale University. CPSC 462/562 is the latest incarnation of my course DragoÅ¡ Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph â¦ I will present a bunch of theorems, a few algorithms, and many open problems. draft, without looking back. NSF CCF-0634957: \Collaborative Research: Spectral Graph Theory and Its Applica- Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial opti- Event description: Theory Seminar. I have chosen to only present material that I consider beautiful. From Applied to Pure Mathematics Algebraic and Spectral Graph Theory Sparsification: approximating graphs by graphs with fewer edges The Kadison-Singer problem . Schur complements, effective resistance and some of their applications. A Social Network Graph . in Computational and Applied Mathematics and a B.S. NSF CCF-0915487: \Spectral Graph Theory, Point Clouds, and Linear Equation Solvers\. I will post a sketch of the syllabus, along with lecture notes, below. Readings for the course will come from drafts of a book that I am writing, and which I will post on this page. AMTH 561/CPSC 662, is a graduate course on Spectral Graph Theory and related topics. Spectral Graph Matching Event time: Friday, October 4, 2019 - 11:00am. Diameter, Doubling, and Applications, Lecture 18. Sekhar Tatikonda Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Graphs and Networks V: a set of vertices (nodes) E: a set of edges an edge is a pair of vertices Dan Preconditioning and the solution of systems of linear equations in graph Laplacians. Textbooks include: I Spectral and Algebraic Graph Theory (Daniel A. Spielman) I Scalable Algorithms for Data and Network Analysis (Shang-Hua Teng) About the Course 5 Objective of the course: I To explore what eigenvalues and â¦ One warning about the lecture notes is in order: I write them in one draft, without looking back. path graphs. Applications to optimization, numerical linear algebra, error-correcting codes, computational biology, and the discovery of graph structure. My Fall 2016 course on algorithmic spectral graph theory. Tutte's rubber band embeddings of planar graphs (11/30/04). Location: Rm 107, 24 Hillhouse Ave. Speaker: Harry Zhou. Spectral and Electrical Graph Theory Daniel A. Spielman Dept. Lecture 2. Department of Statistics and Data Science. Yale University Toronto, Sep. 28, 2011 . It will also include some related content that is not strictly linear algebraic, and some that does not have much to do with graphs, but which I include because it is worth knowing. As a methodological approach, SNA refers to a catalog of techniques steeped in mathematical graph theory and now extending to statistical simulation and algebraic models. preferences. One warning about the lecture notes is in order: I write them in one tral graph theory, Spielman and Teng34 introduced a notion of spectral similarity for two graphs. with examples from Graph Theory." T-Th 2:30-3:45 in AKW 500 (in AKW 207a) T-Th 2:30-3:45 in AKW 500 I will post a sketch of the syllabus, along with lecture notes, below. Sterling Professor of Computer Science and Professor of Statistics & Data Science and of Mathematics AMTH 500, Spectral Graph Theory & Apps: An applied approach to spectral graph theory. Lecture 8. Course website. Fiedler's analysis of the eigenvectors of weighted You could think of this as a course in "Advanced Linear Algebra The course description may be found here. Most lectures will cover some essential element of Linear Algebra or Graph partitioning and Cheeger's inequality. This version of the course will assume less familiarity with a mathematics curriculum. of Computer Science Program in Applied Mathematics Yale Unviersity. At Yale, this probably means Math 244 or CPSC 365, and at least one of Math 230/231, 300 or 301. Christopher Harshaw is a Ph.D. student advised by Professors Daniel Spielman and Amin Karbasi. I love the material in these courses, and nd that I can â¦ At Yale, Jay is working on his PhD in Computational Biology and Bioinformatics. COMPSCI 638: Graph Algorithms October 23, 2019 Lecture 17 Lecturer: Debmalya Panigrahi Scribe: Kevin Sun 1 Overview In this lecture, we look at the fundamental concepts of spectral graph theory. Outline Introduction to graphs Physical metaphors Laplacian matrices Spectral graph theory A very fast survey Trailer for lectures 2 and 3 . Expander graphs, some of their applications, and connections to error-correcting codes. Chris Godsil and Gordon Royle, Algebraic Graph Theory. Yale University 24 Hillhouse Avenue New Haven, CT 06511. t 203.432.0666 f 203.432.0633. Office Hours: Friday, 3:00 - 4:00 . â INTRODUCTIONâ Spectral graph theory starts by associating matrices to graphs, notably, the adja- cency matrix and the laplacian matrix. His research interests are Spectral Graph Theory, Signal Processing, Dimensionality reduction, data visualization. Luca Trevisan, UC Berkeley and Bocconi University Spring 2016. 2018, 2015, 2012, or 2009, 2004. Spectral Graph Theory and its Applications Applied Mathematics 500A . CPSC 662 / AMTH 561: Spectral Graph Theory. To help you decide if this course is right for you, you can look at the lectures notes from the previous versions, taught in 8/1/09-7/31/12. Course notes. You could also think of this as a course in "how to talk with Dan", because Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. Analysis of random walks on graphs, and Poincare inequalities. An introduction to the "animals in the Zoo": the spectra of some fundamental graphs: paths, trees, rings, grids, hypercubes, and random graphs. back to material covered in this course. CHAPTER 1 Eigenvalues and the Laplacian of a graph 1.1. AMTH 561/CPSC 662: Spectral Graph Theory. Instructor: Luca Trevisan, UC Berkeley Stanford course, Winter 2011. CPSC 462/562 is the latest incarnation of my course course on Spectral Graph Theory. Solving Linear Systems (11/9/04), Lecture 19. Dan Spielman, Yale University Fall 2015. Whereas the previous versions, numbered AMTH 561 and CPSC 662, were essentially taught as graduate mathematics courses, this version is suitable for undergraduates and has a more applied focus. Time: M-W 2:30-3:45. The book for the course is on this webpage. Study Log. Jay is currently pursing a postdoctoral fellowship at Yale University. Christopher is interested in spectral graph theory, combinatorial optimization, and applications to machine learning. 2 Spectral Graph Theory The basic premise of spectral graph theory is that we can study graphs by considering their matrix representations. Spectral graph theory is the study and exploration of graphs through the eigenvalues and eigenvectors of matrices naturally associated with those graphs. Note: These plans may change, and I have not yet decided on the content of the last 4 lectures. Whereas the previous versions, numbered AMTH 561 and CPSC 662, were essentially taught as graduate mathematics courses, this version is suitable for undergraduates and has a more applied focus. The less obvious requirements are "mathematical maturity" and "mathematical literacy". This book is mostly based on lecture notes from the \Spectral Graph Theory" course that I have taught at Yale, with notes from \Graphs and Networks" and \Spectral Graph Theory and its Applications" mixed in. In the early days, matrix theory and linear algebra were used to â¦ So, they may contain mistakes and strange grammar. This course surveys the growing field of SNA, emphasizing the merger of theory and method, while gaining hands-on experience with network data and software. The construction of a diffusion process on the graph is a classical topic in spectral graph theory [weighted graph Lapla-cian normalization (8)], and the procedure consists in renor-malizing the kernel k(x, y) as follows: for all x X, let v x X k x, y d y, and set a x, y k x, y v ix. I find that almost every research question I address somehow relates CPSC 531 (Spectral Graph Theory): A graduate course on graph theory covering many theorems, a few algorithms, and many open problems. The obvious prerequisites for this course are knowledge of linear algebra and exposure to graph theory. (in AKW 207a). Note that the undergraduate version, 462, has been approved but does not yet appear in Course Search. But, it sure beats taking notes! Lap Chi Lau, University of Waterloo Fall 2015. course on Spectral Graph Theory. Student and faculty explanations of current research in areas such as random graph theory, spectral graph theory, Markov chains on graphs, and the objective method. Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. Instructor: Dan Spielman. Spielman, Daniel. [email protected] Phone: 203-436-1264 Website Research Interests: Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. Spectral Graph Theory, Fall 2015 Applied Mathematics 561/ Computer Science 662 . Dan Spielman. Credit only with the explicit permission of the seminar organizers. Given a weighted graph = (, V w), we define the G Laplacian quadratic form of to be the function G Q G from RV to R given by If S is a set of vertices and x is the characteristic vector of S Related Jupyter notebooks will appear on this page later. Outline Adjacency matrix and Laplacian Intuition, spectral graph drawing Physical intuition Isomorphism testing Random walks Graph Partitioning and clustering Topics: Cutting graphs and Cheeger's inequality. their Laplacians. Course: Spectral Graph Theory from Yale. We will first describe it as a generalization of cut similarity. Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph Theory. Available in. Jupyter Notebook, and an HTML version of that, and files used in the lecture: dodec.txt; YALE.jld2 Graph partitioning in random models (Stochastic Block Models). Topics: Many examples of graphs and A Social Network Graph . Lectures and Assignments. The general theme is then, ï¬rstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenval- ues to structural properties of graphs. The sections of the book are drawn from my old lecture notes. Spectral Graph Theory and its Applications Daniel A. Spielman Dept. Introduction Spectral graph theory has a long history. Spring 2019. He earned a B.A. Yale University AMS Josiah Willard Gibbs Lecture January 6, 2016 . The main purpose of this course is to explore what eigenvalues and eigenvectors of graphs can tell us about their structure, and to exploit this knowledge for algorithmic purposes. I hope that it will provide a convenient reference for both the course and for lots of exciting material that we will not have time to cover. Preconditioning by augmented trees (11/11/04), Lecture 20. Graph Decomposotions (11/18/04), Lecture 21. From the first lecture in 2009, â this course is about the eigenvalues and eigenvectors of matrices associated with graphs, and their applications. Continuation of the Yale Probability Network Group seminar. Spectral Theory. Course notes from Stanford Winter 2011/2013. Aug. 29: Introduction and course overview. Suggested topics for future lectures, please provide Yale ì ê°ì Spectral Graph Theory(2018 Fall) ìë£ë¥¼ ì ë¦¬í í¬ì¤í¸ìëë¤. matrices. CPSC 662 Spectral Graph Theory Daniel Spielman: MW 2.30-3.45 at WTS A60 : S&DS 600 Advanced Probability Sekhar Tatikonda: TT 2:30-3:45 at ML 211 : CPSC 659 Building Interactive Machines Marynel Vazquez: MW 1.00-2.15 at AKW 200 : CPSC 575 Computational Vision and Biological Perception Dan Spielman, Yale University, Fall 2015. It is intuitively related to attempts to understand graphs through the simulation of processes on graphs and through the consideration of physical systems related to graphs. It does not have many prerequisites, but it should still be viewed as an advanced course. Connections to Spring and Electrical networks. YALE 2004 WORKSHOP on DISCRETE MATHEMATICS and THEORETICAL COMPUTER SCIENCE, Concentration of eigenvalues of random You can find the schedule of lectures and assignments, here. Topics: Lower bounding \lambda_2, and Fall 2018. Contact But, it will still move at a very fast pace. in Electrical Engineering from Rice University. Laplaceâs equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Instructor: Dan Spielman. The combinatorial meaning of the eigenvalues and eigenvectors of matrices associated with graphs. of Computer Science Program in Applied Mathematics Yale Unviersity Lecture 3. It will be taught in the style of a math class. Lecture 4. And assignments, Here draft of Spectral similarity for two graphs order: I write them in draft. With lecture notes is in order: I write them in one draft, looking. 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