(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. Credit only with the explicit permission of the seminar organizers. AMTH 561/CPSC 662, is a graduate course on Spectral Graph Theory and related topics. Course website. Analysis of random walks on graphs, and Poincare inequalities. Course notes. 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. Course: Spectral Graph Theory from Yale. â INTRODUCTIONâ Spectral graph theory starts by associating matrices to graphs, notably, the adja- cency matrix and the laplacian matrix. Event description: Theory Seminar. T-Th 2:30-3:45 in AKW 500 in Electrical Engineering from Rice University. Office Hours: Friday, 3:00 - 4:00 . preferences. Department of Statistics and Data Science. 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. Note that the undergraduate version, 462, has been approved but does not yet appear in Course Search. You could think of this as a course in "Advanced Linear Algebra Time: M-W 2:30-3:45. From the first lecture in 2009, â this course is about the eigenvalues and eigenvectors of matrices associated with graphs, and their applications. AMTH 500, Spectral Graph Theory & Apps: An applied approach to spectral graph theory. Available in. 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. Expander graphs, some of their applications, and connections to error-correcting codes. Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. Readings for the course will come from drafts of a book that I am writing, and which I will post on this page. Lecture 4. A Social Network Graph . 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. Fall 2018. Sekhar Tatikonda Graph Decomposotions (11/18/04), Lecture 21. Lecture 8. Most lectures will cover some essential element of Linear Algebra or 8/1/09-7/31/12. Yale University AMS Josiah Willard Gibbs Lecture January 6, 2016 . Preconditioning and the solution of systems of linear equations in graph Laplacians. At Yale, Jay is working on his PhD in Computational Biology and Bioinformatics. Topics: Lower bounding \lambda_2, and 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 Solving Linear Systems (11/9/04), Lecture 19. 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. hypercubes, and random graphs. At Yale, this probably means Math 244 or CPSC 365, and at least one of Math 230/231, 300 or 301. I find that almost every research question I address somehow relates Yale University 24 Hillhouse Avenue New Haven, CT 06511. t 203.432.0666 f 203.432.0633. Schur complements, effective resistance and some of their applications. 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 with examples from Graph Theory." Graphs and Networks V: a set of vertices (nodes) E: a set of edges an edge is a pair of vertices Dan Jupyter Notebook, and an HTML version of that, and files used in the lecture: dodec.txt; YALE.jld2 Spectral Theory. Contact draft, without looking back. Dan Spielman, Yale University Fall 2015. I love the material in these courses, and nd that I can â¦ 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. Suggested topics for future lectures, please provide of Computer Science Program in Applied Mathematics Yale Unviersity 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. of Computer Science Program in Applied Mathematics Yale Unviersity. The less obvious requirements are "mathematical maturity" and "mathematical literacy". Preconditioning by augmented trees (11/11/04), Lecture 20. Sterling Professor of Computer Science and Professor of Statistics & Data Science and of Mathematics Speaker affiliation: Henry Ford II Professor of Statistics and Data Science, Yale University. YALE 2004 WORKSHOP on DISCRETE MATHEMATICS and THEORETICAL COMPUTER SCIENCE, Concentration of eigenvalues of random Yale University Toronto, Sep. 28, 2011 . Applications to optimization, numerical linear algebra, error-correcting codes, computational biology, and the discovery of graph structure. Aug. 29: Introduction and course overview. Topics: Cutting graphs and Cheeger's inequality. His research interests are Spectral Graph Theory, Signal Processing, Dimensionality reduction, data visualization. But, it will still move at a very fast pace. CPSC 462/562 is the latest incarnation of my course course on Spectral Graph Theory. So, they may contain mistakes and strange grammar. Due to the recent discovery of very fast solvers for these equations, they are also becoming increasingly useful in combinatorial opti- Connections to Spring and Electrical networks. 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. Graph partitioning in random models (Stochastic Block Models). I have chosen to only present material that I consider beautiful. Luca Trevisan, UC Berkeley and Bocconi University Spring 2016. in Computational and Applied Mathematics and a B.S. 2018, 2015, 2012, or 2009, 2004. The sections of the book are drawn from my old lecture notes. path graphs. Jay is currently pursing a postdoctoral fellowship at Yale University. Yale ì ê°ì Spectral Graph Theory(2018 Fall) ìë£ë¥¼ ì ë¦¬í í¬ì¤í¸ìëë¤. My Fall 2016 course on algorithmic spectral graph theory. Topics: Many examples of graphs and course on Spectral Graph Theory. DragoÅ¡ Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph â¦ Spectral graph theory is the study and exploration of graphs through the eigenvalues and eigenvectors of matrices naturally associated with those graphs. The combinatorial meaning of the eigenvalues and eigenvectors of matrices associated with graphs. One warning about the lecture notes is in order: I write them in one draft, without looking back. You can find the schedule of lectures and assignments, here. Introduction Spectral graph theory has a long history. Lectures and Assignments. NSF CCF-0634957: \Collaborative Research: Spectral Graph Theory and Its Applica- It does not have many prerequisites, but it should still be viewed as an advanced course. To help you decide if this course is right for you, you can look at the lectures notes from the previous versions, taught in matrices. Luca Trevisan, UC Berkeley Stanford course, Winter 2011. I will post a sketch of the syllabus, along with lecture notes, below. Instructor: Dan Spielman. An introduction to the "animals in the Zoo": the spectra of some fundamental graphs: paths, trees, rings, grids, 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. Diameter, Doubling, and Applications, Lecture 18. CPSC 531 (Spectral Graph Theory): A graduate course on graph theory covering many theorems, a few algorithms, and many open problems. back to material covered in this course. Spectral Graph Theory and its Applications Daniel A. Spielman Dept. This version of the course will assume less familiarity with a mathematics curriculum. Dan Spielman, Yale University, Fall 2015. We will first describe it as a generalization of cut similarity. Related Jupyter notebooks will appear on this page later. NSF CCF-0915487: \Spectral Graph Theory, Point Clouds, and Linear Equation Solvers\. CPSC 462/562 is the latest incarnation of my course Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph Theory. Outline Adjacency matrix and Laplacian Intuition, spectral graph drawing Physical intuition Isomorphism testing Random walks Graph Partitioning and clustering Fiedler's analysis of the eigenvectors of weighted The course description may be found here. The book for the course is on this webpage. Study Log. CPSC 662 / AMTH 561: Spectral Graph Theory. 2 Spectral Graph Theory The basic premise of spectral graph theory is that we can study graphs by considering their matrix representations. Continuation of the Yale Probability Network Group seminar. Tutte's rubber band embeddings of planar graphs (11/30/04). 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¦ Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. The obvious prerequisites for this course are knowledge of linear algebra and exposure to graph theory. (in AKW 207a). CHAPTER 1 Eigenvalues and the Laplacian of a graph 1.1. Note: These plans may change, and I have not yet decided on the content of the last 4 lectures. From Applied to Pure Mathematics Algebraic and Spectral Graph Theory Sparsification: approximating graphs by graphs with fewer edges The Kadison-Singer problem . 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. their Laplacians. Chris Godsil and Gordon Royle, Algebraic Graph Theory. I will present a bunch of theorems, a few algorithms, and many open problems. AMTH 561/CPSC 662: Spectral Graph Theory. Instructor: Spectral Graph Theory and its Applications Applied Mathematics 500A . Dan Spielman. 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. It will be taught in the style of a math class. Laplaceâs equation and its discrete form, the Laplacian matrix, appear ubiquitously in mathematical physics. Christopher Harshaw is a Ph.D. student advised by Professors Daniel Spielman and Amin Karbasi. Spring 2019. But, it sure beats taking notes! Lecture 2. daniel.spielman@yale.edu Phone: 203-436-1264 Website Research Interests: Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. Outline Introduction to graphs Physical metaphors Laplacian matrices Spectral graph theory A very fast survey Trailer for lectures 2 and 3 . Spectral Graph Matching Event time: Friday, October 4, 2019 - 11:00am. Analysis of algorithms and heuristics, error-correcting codes, combinatorial scientific computing, spectral graph theory, and combinatorics. He earned a B.A. In the early days, matrix theory and linear algebra were used to â¦ 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. One warning about the lecture notes is in order: I write them in one A Social Network Graph . Lecture 3. Course notes from Stanford Winter 2011/2013. 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. You could also think of this as a course in "how to talk with Dan", because tral graph theory, Spielman and Teng34 introduced a notion of spectral similarity for two graphs. Spielman, Daniel. Location: Rm 107, 24 Hillhouse Ave. Speaker: Harry Zhou. 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