Yufei zhao mit Massachusetts Institute of Technology Verified email at mit. Link to Canvas. Geometric and Functional Analysis, 31(5), 1160-1218. We explore an intimate connection between Young tableaux and representa-tions of the symmetric group. We study a number of surprising applications of polynomials to problems in combinatorics. (2019), 172–195 blog MIT News; A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner) Determinants: Evaluation and Manipulation - MIT UMA Putnam Talk; Linear algebra tricks for the Putnam - MIT UMA Putnam Talk; Combinatorics. Each section focuses on a different technique, along with examples of applications. Yufei Zhao • Explored Ruzsa’s conjecture; improved bounds and established new links to arithmetic Ramsey problems. Time and Location: Please check the Google calendar below for the definitive schedule. MIT graduate course taught by Prof. Yufei received his dual SB degrees in Mathematics and Computer Science from MIT in 2010, an MASt in Mathematics from Cambridge in 2011, and a PhD from MIT in 2015, under the supervision of Jacob Fox. Feb 28, 2025 · MIT’s success in the Putnam exam isn’t surprising. Points X;Y, and Z lie on sides BC;CA MIT OpenCourseWare is a web based publication of virtually all MIT course content. edu 1 Warm up problems 1. He then takes the class on a tour of modern highlights of the field: Roth’s theorem, Szemerédi’s theorem, and the Green–Tao theorem. Feb 22, 2018 · The Institute's Putnam exam preparation was run by Yufei Zhao SB '10, PhD '15, who was recently appointed as an assistant professor in the MIT Department of Mathematics. Then AD coincides with a symmedian of 4ABC. Contents Preface v NotationandConventions ix 0 Appetizer:TrianglesandEquations 1 0. Lecturer: Yufei Zhao (see website for contact info) Office hours: After lectures or by email appointment. edu Jonathan Tidor Stanford University Verified email at stanford. edu 1 Bijections Basic examples 1. Looking at the coe cients Bound the size of the coe cients Mar 11, 2022 · It’s an amazing accomplishment,” says Yufei Zhao, assistant professor of mathematics, who oversees the competition at MIT and also coaches first-year students for the competitions via class 18. Instructor: Yufei Zhao Professor Yufei Zhao, who took 18. “The results of the Putnam are a source of pride for our institution and a reflection of Yufei Zhao. “I am incredibly proud of our students’ amazing effort and performance at the Putnam Competition,” says associate professor of mathematics Yufei Zhao ’10, PhD ’15. 217 Graph Theory and Additive Combinatorics Fall2019 Yufei Zhao Created Date: 20200309212336Z Fall 2018, MIT. Indeed, many geometry problems are built on a few common themes. IMO Training 2008 Combinatorics Yufei Zhao Combinatorics July 6, 2008 Yufei Zhao yufeiz@mit. Let ABC be a triangle and its circumcircle. (AM-GM) Let a 1; ;a nbe positive real numbers. Lecturer: Yufei Zhao (see website for contact info). Exponential improvements for superball packing upper bounds. 211” in the subject line of your emails. Please include “18. 编辑：LRS 【新智元导读】解决一个七十年悬而未决的问题需要多久？答案显然不是七十年。最近MIT著名华人数学副教授Yufei Zhao带领两名本科生只用了一个暑假就完全攻克图论中的等角线问题，为后续计算机图发展奠定基础。 This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Textbook: Yufei Zhao, Graph Theory and Additive Combinatorics: Exploring Structure and Randomness, Cambridge University Press, 2023 Lecture video recordings from Fall 2019 (may not correspond exactly to the current semester) may be found on MIT OpenCourseWare and YouTube . Then AD coincides with a symmedian of ABC. Special office hours will be set up before homework due dates. Yufei Zhao (MIT) Eigenvalues of Random Graphs May 2012 3 / 46. Zhao conducts research in discrete mathematics. A reverse Sidorenko inequality. Zhao credits Stanley for creating high-quality problem sets, which are still being used in the seminar. edu We will use Z[x] to denote the ring of polynomials with integer coe cients. Many of these results were discovered only in the past decade, and their solutions are often Yufei Zhao: Dénes König Prize, SIAM: Yufei Zhao: The Future of Science Award, MIT School of Science: Yufei Zhao: Class of 1956 Career Development Professorship Chair: Yufei Zhao: Best Paper Award, ICCM Lecturer: Professor Yufei Zhao Notes by: Andrew Lin Spring 2019 This is an edited transcript of the lectures of MIT’s Spring 2019 class 18. Please share how this access benefits you. Location: C3 (week 1), C4 (weeks 2—8) Mathematical Institute, University of Oxford. Location: Wilfrid Laurier University in Waterloo, Ontario Dates: June 27 to July 9, 2008 Summer camp participants, including local students This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Then, we have a 1 + + a Yufei Zhao; Administrative Assistant: Ian Wang, mjwang79@mit. Contents 1 Introduction 2 Instructor: Yufei Zhao View the complete course: https://ocw. (IMO Shortlist 1997) Let fbe a polynomial with integer coe cients and let pbe a prime such that f(0) = 0, f(1) = 1, and f(k) 0 or 1 (mod p) for all positive integers k. Talks take place at MIT and Harvard. Fall 2020, MIT (Link to the most current version of the course) Class meetings: Mondays and Wednesdays 10–11am (Note time change) Instructor: Yufei Zhao (see link for contact info) Assistants: Dain Kim and Daniel Zhu. Yufei Zhao, the Class of 1956 Career Development Assistant Professor in the Department of Mathematics, has been named the second recipient of the MIT School of Science’s Future of Science Award. A34 (Mathematical Problem Solving, Putnam Seminar). 218: The Probabilistic Method in Combinatorics, taught by Professor Yufei Zhao. (Miquel’s theorem) Let ABC be a triangle. MIT OCW: Graph Theory and Additive Combinatorics --- Yufei Zhao. INTRODUCTION Yufei Zhao at MIT in Fall 2019. And Zhao is also continuing Stanley’s goal to steer students away from seeing the seminar as simply training for Putnam. Course description and policies MOP 2007 Black Group Counting in Two Ways Yufei Zhao Counting in Two Ways Incidence Matrices June 26, 2007 Yufei Zhao yufeiz@mit. Additional course material, IMO Training 2007 Lemmas in Euclidean Geometry Yufei Zhao Lemmas inEuclideanGeometry 1 Yufei Zhao yufeiz@mit. edu Yufei Zhao Massachusetts Institute of Technology Verified email at mit. com YUFEI ZHAO p. 225 Graph Theory and Additive Combinatorics (grad), Fall 2023 Book Exercises MIT OCW YouTube; 18. 217 F2019 Full Lecture Notes: Graph Theory and Additive Combinatorics | Graph Theory and Additive Combinatorics | Mathematics | MIT OpenCourseWare Reviews ‘Yufei Zhao does great mathematics and has an uncanny ability to explain the deepest results with clear understandable prose. Let ABCbe a triangle and Γ its circumcircle. Eigenvalues of random graphs Random d-regular graph G n;d Largest eigenvalue is d 强烈推荐MIT大神Yufei Zhao上个学期的课程讲义，Graph Theory and Additive Combinatorics。 这个讲义的每一节我都仔细读过，知识更新得非常迅速，其中已经包含很多2019年下半年的新结果。经典的内容都写得非常好，而且我非常喜欢里面的那张配图。 Winter Camp 2009 Cyclic Quadrilaterals Yufei Zhao Cyclic Quadrilaterals | The Big Picture Yufei Zhao yufeiz@mit. Inventiones mathematicae, 221(2), 665-711. *Graph Theory and Additive Combinatorics: Exploring Structure and Randomness*. Let AB and CD be two segments, and let lines AC and BD meet at X. A34 Mathematical Problem Solving (Putnam Seminar) as an undergraduate at MIT and was a three-time Putnam Fellow, has gone on to a flourishing career in mathematics: Yufei Zhao Wins Future of Science Award. 2023. Four from MIT Named 2019 Sloan Research Fellows IMO Training 2008 Polynomials Yufei Zhao 10. Tagged: Yufei Zhao. This year’s cohort brings MIT’s total to nearly 300 fellows — more than any single institution in the history of the fellowships. Default locations are MIT Room 2-135 or Harvard Science Center Room 232 on Wednesdays, and MIT Room 2-139 on Thursdays. Course description Feb 23, 2023 · “Our students' outstanding performance on the Putnam is a testament to their dedication and hard work,” says Yufei Zhao, associate professor of mathematics, who prepares a group of first-year students for the competition through his Putnam Seminar. edu 1. e. Tiling - MOP 2007 Blue group Discussion of tiling Mar 1, 2024 · There were also 52 MIT students in the 201-500 finishers. Paper underreviewatMPCPS. MIT; Supervised by Prof. (Article in MIT News) Vishesh Jain, A. edu - Homepage. The notes were written by the students of the class based on the lectures, and edited with the help of the professor. Quick links: [Problem set] Class meetings: Mondays and Wednesdays 2:30–4pm, room 4-153 Content created by the MIT Libraries, Zhao, Yufei. We describe the construction of Specht modules which are irreducible representations of Sn, and also highlight some interesting results such as the branching rule and Young’s rule. Mar 4, 2019 · The class is taught by Zhao ’10, PhD ’15, a three-time Putnam Fellow who took the same class under professors Richard Stanley and Hartley Rogers. Yufei works on problems in extremal combinatorics, spectral graph theory, and discrete geometry. Andy works on understanding the asymptotic dynamics of solutions to partial differential equations. edu 1 Classical Theorems Theorem 1. Other than those listed below, all problem sets were created by anonymous guest lecturers. Advisor: Yufei Zhao (MIT) Research Interests: Extremal and probabilistic combinatorics. https://ocw. 1 Schur’sTheorem 1 0. Let the tangent to at B and C meet at D. October 23: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. Four-peat: MIT students take first place in the 84th Putnam Math Competition Read it at MIT News. vi Preface A core thread throughout the book is the connection bridging graph theory and additive The MIT team, consisting of Qingchun Ren, Xuancheng Shao, and Yufei Zhao placed third after Harvard University and Princeton University. 18. It is a prestigious award based on his research contribution to the field of combinatorics – as well as his mentorship, service and outreach. home cv research blog. OCW: How did you approach designing and teaching this course? Yufei Zhao: This is the second iteration of a course I first taught two years ago. (2006/G2) Let ABCD be a trapezoid with parallel sides AB > CD. Advances in Mathematics, 365, 107056. Used with permission. OCW is open and available to the world and is a permanent MIT activity 18. edu A large number of combinatorics problems involve looking at a quantity in at least two di erent ways. Eigenvalues of random graphs Random d-regular graph G n;d Largest eigenvalue is d MOP 2007 Black Group Integer Polynomials Yufei Zhao Integer Polynomials June 29, 2007 Yufei Zhao yufeiz@mit. Instructor: Prof. “It was a pretty surreal result. Dec 14, 2022 · When he returned to MIT in 2017 to join the faculty, he began teaching the Putnam Seminar. 2. The notes have not been thoroughly checked for accuracy, espe-cially attributions of results. Abstract: Starting with Schur's attempt from a hundred years ago at proving Fermat's Last Theorem, we explore connections between graph theory on one hand, and an area of number theory known as additive combinatorics on the other hand. Acknowledgements. edu Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. Prove that triangles OAB and OCD are similar. Friday, January 8: Yufei Zhao. But they aren’t limitless, according to Zhao and his team of MIT mathematicians, who sought to solve this problem on the geometry of lines in high-dimensional space. After k>1 groups have gone, every two students have gone together exactly once. mit. “We are very proud of the academic excellence of our students, and we celebrate the results of Oct 10, 2021 · 来源：MIT. Equiangular lines Joints Extension complexity Width of transitive sets. Citation: Jiang, Zilin, Tidor, Jonathan, Yao, Yuan, Zhang, Shengtong and Zhao, Yufei. March 01, 2024. Yufei Zhao; Departments Mathematics; As Taught In Fall 2018 (Image adapted by MIT OpenCourseWare from Supplementary Problems #3 (PDF). Course description. Ting-Wei Chao Extremal Combinatorics, Incidence Geometry; Manik Dhar Combinatorics, Theoretical Computer Science; Siddarth Kannan Algebraic geometry, Combinatorics; Sammy Luo Extremal and additive combinatorics IMO Training 2008 Geometry Yufei Zhao Selected Geometry Problems from Recent IMO Shortlists 1. Sah, Mehtaab Sawhney, David Stoner, and Yufei Zhao. He solved an open problem in graph theory, simplified the proof of the Green-Tao theorem, and advised the winning team of the Putnam Mathematics Competition. The course focuses on methodology as well as combinatorial applications. , P a2A 1=a, must contain arbitrarily long APs. Your story matters. Undergraduate Assistants (UA): Mark Saengrungkongka and Tomasz Slusarczyk. edu A Taste of Algebraic Combinatorics Problem: (St. IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. (The symmedian is the re ection of the median seems like he posted on ejmr and the reddit thread at the same time, updating us on yufei’s current employer 4 months ago # QUOTE 0 Good 0 No Giod ! Economist Yufei Zhao (MIT) Eigenvalues of Random Graphs May 2012 3 / 46. (AM-GM) Let a 1; ;a n be positive real numbers. 225 官方主页找到原始讲义和其他课程相关内容。 Jun 27, 2008 · Canadian IMO Summer Training Camp 2008. This conjecture is widely believed to be true, but it has yet to be proved even in the case of 3-term APs2. Course description A. Research. edu 18. Lecturer: Yufei Zhao (see link for contact info) Spring 2019, MIT (Link to the most current version of the course) Class meetings: Tuesdays and Thursdays 2:30–4pm in 3-370. Cambridge University Press, 2023. 1 ForbiddingaTriangle:Mantel’sTheorem 12 MIT Team Wins Putnam, Five Named Putnam Fellows Mathematics Professor Yufei Zhao, far right, stands with winners of the 78th annual William Lowell Putnam Mathematical Competition. In the 1930’s, Erdos˝ and Turán conjectured a stronger statement, Erdos˝ and Turán (1936) Instructor: Yufei Zhao. October 21: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. Office hours: M 2:45-3:45pm & TR 2:30-3pm in 2-271. (The symmedian is the reflection of the median MIT OpenCourseWare is a web based publication of virtually all MIT course content. Class meetings: Tuesdays and Thursdays 1–2:30pm in 2-135. Zhao is also a three-time Putnam Fellow. S Zhang, Y Zhao. MIT wins 83rd Putnam 2 DAVID CONLON, JACOB FOX, AND YUFEI ZHAO with divergent harmonic sum, i. 16 highlights from additive combinatorics that there are no infinitely long monochromatic arithmetic progres-sions. Yufei Zhao. The course also introduces students to current research topics and open problems. Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. Professor Zhao begins the course with a proof of Schur’s theorem via graph theory and how it led to the modern development of additive combinatorics. edu/18-217F19 This course examines classical and modern developments in graph theory and add A. We begin by summarizing some of the common approaches used in dealing with integer polynomials. 30. Additional course material, This is an author's version of the textbook. 2021年暑假，我决定尝试翻译赵宇飞（Yufei Zhao）的讲义 Graph Theory and Additive Combinatorics 并得到了伙伴@武弘勋 的支持，您可以直接查看 MIT18. Yufei Zhao MIT Open Access Articles Spherical Two-Distance Sets and Eigenvalues of Signed Graphs The MIT Faculty has made this article openly available. Then, we have a 1 + + a Yufei Zhao April 20, 2011 Abstract We provide an expository account of Furstenberg’s ergodic theoretic proof of Szemer edi’s theorem, which states that every subset of the integers with positive upper density contains arbitrarily long arithmetic progressions. 2 Progressions 5 0. The Putnam Fellows for this year were Bohua Zhan and Yufei Zhao. They are intended to serve as study resources and not as a substitute for professionally prepared publica- IMO Training 2008 Polynomials Yufei Zhao 10. Zhao was named a Putnam Fellow in 2006, 2008, and 2009. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. Winter Camp 2009 Cyclic Quadrilaterals Yufei Zhao Cyclic Quadrilaterals | The Big Picture Yufei Zhao yufeiz@mit. From left are Junyao Peng, Yunkun Zhou, Sammy Luo, Allen Liu, Jiyang Gao, Ashwin Sah, and Omer Cerrahoglu. 217 Graph Theory and Additive Combinatorics. (Article in MIT News) Apr 19, 2024 · Michel Goemans, at left, and Yufei Zhao congratulate Isabella Zhu, who is holding her award for earning the Elizabeth Lowell Putnam Prize. All supplementary problems, Hidden independence and uniformity problems, Probability problems, and additional topics assignments from previous editions are based on files created by Prof. Three of the next eleven highest ranking individuals were MIT students: Qingchun Ren, Colin Sandon, and Jacob Steinhardt. Let the circumcircles of ABX and CDX meet again at O. Prof. Teaching assistants: Pro Pakawut Jiradilok and Morris Jie Jun Ang. Petersburg) Students in a school go for ice cream in groups of at least two. ) Download Course. OCW is open and available to the world and is a permanent MIT activity MIT OpenCourseWare. Looking at the coe cients Bound the size of the coe cients. My goal was to put together a cohesive introduction to an area of modern This course is a graduate-level introduction to the probabilistic methods, a fundamental and powerful technique in combinatorics and theoretical computer science. YUFEI ZHAO ABSTRACT. IMO Training 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. Construction of the symmedian. The Boolean satisfiability problem, specifically k-SAT, occupies a central place in theoretical computer science. 1. Zhao, Yufei. edu An important skill of an olympiad geometer is being able to recognize known con gurations. Yufei Zhao MIT CanaDAM 2021. MIT is also a top destination for medalists participating in the International Mathematics Olympiad (IMO) for high school students. (a) Let n be a positive integer. " In this note, we will mainly focus on how to use incidence Virginia Vassilevska Williams MIT Verified email at mit. In how many ways can one write a sum of at least two positive integers that add up to n? Consider the same set of integers written in a di erent order as being di erent. 3 What’sNextintheBook? 9 1 ForbiddingaSubgraph 11 1. Yufei Zhao joined the mathematics faculty as Assistant Professor in July 2017. Triangles and Equations. Richard Stanley in earlier versions of the course. "I am incredibly proud of MIT students' amazing performance," says Zhao. Let the tangent to Γ at Band Cmeet at D. OCW is open and available to the world and is a permanent MIT activity Yufei Zhao Extremal, probabilistic, and additive combinatorics; Instructors & Postdocs. DownloadThis package contains the same content as the online version of the course, except for the audio/video MOP 2007 Black Group Integer Polynomials Yufei Zhao Integer Polynomials June 29, 2007 Yufei Zhao yufeiz@mit. Sah, and Mehtaab Sawhney. Supervised Program for Alignment Research Mar2023–Aug2023 Berkeley AI Safety; Supervised by Joe Benton Jul 26, 2008 · IMO Training 2007 Lemmas in Euclidean Geometry Yufei Zhao Lemmas in Euclidean Geometry 1 Yufei Zhao yufeiz@mit. 4MB) and the notes by topic below were written by the students of the class based on the lectures and edited with the help of Professor Yufei Zhao. A. Lecture videos on MIT OpenCourseWare and YouTube (Lecture Notes) Probabilistic Methods in Combinatorics Teaching. A34 Mathematical Problem Solving (Putnam Seminar), Fall 2023 MIT News Profile Putnam Competition results 2023, 2022, 2021, 2019 Bio. Time: Tuesday 10—11. Fall 2021, MIT, graduate level (Link to the most current version of the course). Then, we have a 1 + + a MIT OpenCourseWare is a web based publication of virtually all MIT course content. " In this note, we will mainly focus on how to use incidence IMO Training 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. This course was previously numbered 18. Blog of Yufei Zhao, Associate Professor of Mathematics at MIT. Bijections; Algebraic Techniques in Combinatorics - MOP 2007 Black Group Applications of linear algebra and posets to olympiad-style combinatorics problems. See full list on yufeizhao. I will show the proof of Schur's theorem, and take you Winter Camp 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. Prove that the number Sep 6, 2018 · Yufei Zhao won the MIT School of Science’s Future of Science Award over the summer. Annals of Mathematics 194 (3), 729-743, 2021. Feb 21, 2019 · Nikhil Agarwal, Andrew Lawrie, Yufei Zhao, and Daniel Harlow recently received 2019 Sloan Research Fellowships. “This was unprecedented,” says Yufei Zhao, Class of 1956 Career Development Assistant Professor of Mathematics, who coaches first-year students for the competitions via the Putnam Seminar in the fall, and also oversees the competition at MIT. Feb 25, 2019 · In 2009, when Yufei Zhao was an MIT undergraduate, he was intrigued by a 2001 conjecture by Rutgers University mathematician Jeff Kahn regarding the number of independent sets in a graph. In this lecture, we will explore one such con guration. For anyone interested in the seminal ideas (and their interrelationships) of recent decades - pseudorandomness, graphons, graph regularity, to name a few - this is the book to read and savor. 这次论文背后的团队导师赵宇飞（Yufei Zhao），在武汉出生，1999年随父母移民加拿大。 据中新网报道，赵宇飞在中学时被选入资优班，他的数学老师表示“15年间，从未给过学生满分，直至遇到他”。 目前，赵宇飞在MIT任助理教授。 MOP 2007 Black Group Counting in Two Ways Yufei Zhao Counting in Two Ways Incidence Matrices June 26, 2007 Yufei Zhao yufeiz@mit. He also ranked seventh in 2007. 3 of 12 Mingyang Deng ’24 (2022–2023) → MIT CS PhD Tomasz Slusarczyk ’25 (2022) Aleksandre Saatashvili ’23 (2022–2023) → CMU Math PhD Saba Lepsveridze ’24 (2022–2023) → MIT Math PhD MIT students dominate the Putnam Math Competition once again! 🍾 - Top five winners (Fellows) all come from MIT, including: - 3rd time Fellow for… Shared by Yufei Zhao View Yufei’s full profile Jul 9, 2018 · Yufei Zhao, an assistant professor of mathematics at MIT, is honored for his research in discrete mathematics, teaching, service, and outreach. A34” in the subject line of your emails. edu. Of the three non-MIT Putnam Fellows, all from Harvard this year, two also have strong MIT ties as 2014 Oct 4, 2021 · “In high dimensions, things really get interesting, and the possibilities can seem limitless,” says Yufei Zhao, assistant professor of mathematics. OCW is open and available to the world and is a permanent MIT activity Andrew Lawrie and Yufei Zhao were promoted to Associate Professor without Tenure. Fall 2023, MIT [Dropbox (schedule & homework PDFs)] Class meetings: Mondays and Wednesdays 1–2pm, room 2-132. Singularity of discrete random matrices. The MIT team, consisting of Qingchun Ren, Xuancheng Shao, and Yufei Zhao placed third after Harvard University and Princeton University. 76: This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. Below, Professor Yufei Zhao describes various aspects of how he taught 18. This technique is often called \double counting. ’ Fall 2019, MIT (Link to the most current version of the course) Quick links: [Lecture videos: MIT OCW, YouTube] Class meetings: Mondays and Wednesdays 2:30–4pm in 2-190. The top-scoring female in the 2023 annual William Lowell Putnam Mathematical Competition is first-year Isabella Zhu, who received the Elizabeth Lowell Putnam Prize for her efforts. 217. Zhao shares test-taking strategies, and students practice with past years’ Putnam exams. Emails: For quick questions, ask me after class The full lecture notes (PDF - 1. MIT OpenCourseWare is a web based publication of virtually all MIT course content. Tristan Collins, left, received the Class of 1948 Career Development This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. October 25: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. Zilin Jiang, Jonathan Tidor, me, Yuan Yao, Shengtong Zhang. October 28: Charles River Lectures on Probability Theory and Related Topics in E51 MIT Tang Center. An independent set in a graph is a subset of vertices such that no two of them are joined by an edge. MIT’s recent Putnam coaches are four-time Putnam Fellow Bjorn Poonen and three-time Putnam Fellow Yufei Zhao ’10, PhD ’15. Lecturer: Yufei Zhao Notes by: Andrew Lin Spring 2019 This is an edited transcript of the lectures of MIT’s Spring 2019 class 18. nif emj plmlmib iakc jhqdvi fsfoqu uhll uwbv sdmt jzwsjq okz qmrlljqj icixm mmsrk ormqr