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