Yufei zhao mit 194 (2021), 729–743. edu Abstract In this note, we give a short proof of the fact that the coe cients of the polynomial A n(x) = (1 x)(1 x2)(1 x3) (1 xF n)(1 xF n+1) are all equal to 1;0 or 1, where F n is the n-th Fibonacci number. MIT could do better. INTRODUCTION A. 338 Project Spectral Distributions of Random Graphs Yufei Zhao May 2012 1 Introduction Given a graph G with n vertices, its adjacency matrix A(G)is the n n matrix whose (i, j)entry is 1 if vertices i and j are adjacent, and 0 otherwise. A reverse Sidorenko inequality. 218: The Probabilistic Method in Combinatorics, taught by Professor Yufei Zhao. With high probability, most of the middle sums and di erences will be present. Through the seminar, Zhao encourages students to “use their experience in math competitions as a Green proved the following strengthening of Roth's theorem: for every positive ϵ, there is some n(ϵ) such that for every N ≥ n(ϵ) and A ⊂ [N] with |A| = αN, The University of Chicago Department of Mathematics presents a talk by Yufei Zhao (MIT) titled "Equiangular Lines and Eigenvalue Multiplicities. Yufei Zhao MIT CanaDAM 2021. MOP 2007 Black Group Integer Polynomials Yufei Zhao Integer Polynomials June 29, 2007 Yufei Zhao yufeiz@mit. edu 1 Classical Theorems Theorem 1. Class meetings: Tuesdays and Thursdays 3–4pm in 2-147 Instructor: Yufei Zhao (see website for contact info) Grader: Yau Wing Li Please include “18. A graduate-level introduction to the probabilistic method, a 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. (17. This year’s cohort brings MIT’s total to nearly 300 fellows — more than any single institution in the history of the fellowships. 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. Yufei Zhao Undergraduate Assistants (UA): Dain Kim and Tomasz Slusarczyk Emails and Slack: For quick questions, ask me after class; Include both UAs in all class related communication, including everything homework related MOP 2007 Black Group Counting in Two Ways Yufei Zhao Counting in Two Ways Incidence Matrices June 26, 2007 Yufei Zhao yufeiz@mit. A progression of theorems on progressions van der Waerden’s theorem (1927) If N is colored with nitely many colors, then there are arbitrarily long monochromatic Content created by the MIT Libraries, CC BY-NC unless otherwise noted. His work is unimpressive. He received his PhD from MIT in 2015 and has previously held positions at Oxford, Berkeley, Stanford, and Microsoft Winter Camp 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. In this paper, we determine the tight constant in the joints problem. Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. 2. DownloadThis package contains the same content as the online version of the course, except for the audio/video materials. Other than those listed below, all problem sets were created by anonymous guest lecturers. Thue's proof part III Introduction to the Kakeya problem 29. Zilin Jiang, Jonathan Tidor, me, Yuan Yao, Shengtong Zhang. Class meetings: Tuesdays and Thursdays 2:30–4pm in 3-370 Lecturer: Yufei Zhao (see website for contact info) Office hours: After lectures or by email appointment. Research. home cv research blog. 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. Primary DLC. Then MI is a midline of triangle XYD, so IM and YD are parallel. MIT Room: 2-271 (617) 253-4380. Sign up to receive news and updates from MIT Industrial Liaison Program Sign up. Andy works on understanding the asymptotic dynamics of solutions to partial differential equations. edu Editor-in-chief: Gwen McKinley gweneth@mit. This course was previously numbered 18. (The symmedian is the re ection of the median Yufei Zhao won the MIT School of Science’s Future of Science Award over the summer. Link to Canvas. Yufei Zhao MIT Equiangular lines and eigenvalue multiplicity Abstract: Equiangular lines are configurations of lines in n-dimensional space, all passing through the origin, that pairwise make the same angle. Due: Hidden independence and uniformity & SS3. Let pbe a prime. Computer Science and Engineering, Yufei Zhao joined the mathematics faculty as Assistant Professor in July 2017. I earned my undergraduate complexity under the guidance of Prof. Department of Mathematics. Additional links to my work: (2019), 172–195 blog MIT News; A reverse Sidorenko inequality (with Ashwin Sah, Mehtaab Sawhney, and David Stoner) Yufei Zhao's notes on algebra, combinatorics, geometry, and number theory for math olympiad training. Left to right: Coach Yufei Zhao poses with winners Ashwin Sah, Shengtong Zhang, Yuan Yao, Acknowledgements. Let r = (r. Ting-Wei Chao Extremal Combinatorics, Incidence Geometry; Manik Dhar Combinatorics, Theoretical Computer Science; Siddarth Kannan Algebraic geometry, Combinatorics; Sammy Luo Extremal and additive combinatorics Winter Camp 2010 Three Lemmas in Geometry Yufei Zhao Solution: Let the incircle of ABC touch BC at X, and let XY be a diameter of the incircle. Blog. D. Let AB and CD be two segments, and let lines AC and BD meet at X. Two other MIT Elizabeth Putnam Prize winners are Ruth A. Points X;Y, and Z lie on sides BC;CA Yufei Zhao tenured at MIT. Citation: Zhao, Yufei. edu Lec 1, 9/7: Yufei Zhao yufeiz@mit. Hung-Hsun Hans Yu. And even more recently, During my undergraduate and master years, I had the great fortune to be mentored by Yufei Zhao, Dor Minzer, Sam Hopkins, Henry Cohn, Lisa Sauermann, Adam Sheffer, Kuikui Liu and Marcelo Campos. Learning Resource Types assignment Problem Sets. MIT; Supervised by Prof. Then, we have a 1 + + a n n n p a 1 a n: Winter Camp 2008 Inequalities Yufei Zhao We have @f @a = p a2 + 8bc pa2 a2+8bc a2 + 8bc The MIT team, consisting of Qingchun Ren, Xuancheng Shao, and Yufei Zhao placed third after Harvard University and Princeton University. Class time: Tuesdays and Thursdays 9:30—11am Location: 66-144 (Room change! Lecturer: Yufei Zhao (see website for contact info). Thue's proof part II: polynomials of two variables 28. Since 2a+1 is coprime to 1 3 (2 b+1), the number M= 1 3 (2 a+1)(2b+1) must have at least 24k 1 divisors (for each divisor dof 2a+1, we get two divisors . My papers are listed below by topic. “That was a very nice solution,” math professor Yufei Zhao told the class. Mathematics, MIT, 2015 (Advisor: Jacob Fox) M. "Abstract:Sol At MIT there is literally a course that prepares you for Putnam - literally search for MIT Putnam seminar. Primarily based on problem sets. 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. The course also introduces students to current research topics and open problems. Yufei Zhao; Administrative Assistant: Yufei An, yfa@mit. Paper underreviewatMPCPS. ’ MOP 2007 Black Group Counting in Two Ways Yufei Zhao Counting in Two Ways Incidence Matrices June 26, 2007 Yufei Zhao yufeiz@mit. YUFEI ZHAO PROBLEM SET A. Talks take place at MIT and Harvard. The course examines classical and modern developments in graph theory and additive combinatorics, with a focus PROBABILISTIC METHODS IN COMBINATORICS MIT 18. Class meetings: Mondays and Wednesdays 10–11am (Note time change) Instructor: Yufei Zhao (see link for contact info) Assistants: Dain Kim and Daniel Zhu Please include “18. OCW: You structured problem sets a little differently in this course, providing students with a single file with many problems but only requiring a subset of these problems to be turned in for assessment. Economist Stiglitz. But they aren’t limitless, according to Zhao and his team of MIT Yufei Zhao. Winter Camp 2009 Cyclic Quadrilaterals Yufei Zhao Cyclic Quadrilaterals | The Big Picture Yufei Zhao yufeiz@mit. A34 is a first-year undergraduate seminar on mathematical problem solving. I am fortunate to be advised by Pablo Parrilo and Yufei Zhao. edu A large number of combinatorics problems involve looking at a quantity in at least two di erent ways. edu Nitya Mani. I completed my Ph. Postcode: Yufei Zhao is a Junior Research Fellow in Mathematics at New College, Oxford. Yufei Zhao; Departments Mathematics; As Taught In Fall 2018 Level Undergraduate. seems like he posted on ejmr and the reddit thread at the same time, updating us on yufei’s current employer 1 month ago # QUOTE 0 Good 0 No Giod ! Economist The MIT team, consisting of Qingchun Ren, Xuancheng Shao, and Yufei Zhao placed third after Harvard University and Princeton University. 211 Combinatorial Analysis. Petersburg) Students in a school go for ice cream in groups of at least two. edu A Taste of Algebraic Combinatorics Problem: (St. Y Zhao. . MIT OCW is not responsible for any content on third party sites, nor does a link suggest an endorsement of those sites and/or their content. M 9/27 Discussion — Presentations. 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. 7 months ago # QUOTE 7 Good 4 No Giod! Economist MIT OpenCourseWare is a web based publication of virtually all MIT course content. The collection of eigenvalues of G are also ‘Yufei Zhao does great mathematics and has an uncanny ability to explain the deepest results with clear understandable prose. In Fall 2017, MIT (Link to the most current version of the course). (Cyclotomic polynomials) For a positive integer n, de ne the polynomial n(x) by n(x) = Y Yufei Zhao received this year’s UROP Outstanding Mentor Award, presented to research mentors who have demonstrated exceptional guidance and teaching in a research setting. 14. Looking at the coe cients Bound the size of the coe cients MIT OpenCourseWare is a web based publication of virtually all MIT course content. edu http://yufeizhao. Donner Yufei Zhao, an assistant professor of mathematics at MIT, is honored for his research in discrete mathematics, teaching, service, and outreach. arXiv:1809. (Miquel’s theorem) Let ABC be a triangle. , Cambridge MA, 02142, USA yufeiz@mit. Class meetings: Tuesdays and Thursdays 1–2:30pm in 2-135 Lecturer: Yufei Zhao (see website for contact info). Yufei works on problems in extremal combinatorics, spectral graph theory, and discrete geometry. If not by density considerations, how do Green and Tao prove their theorem? Fall 2020, MIT (Link to the most current version of the course). Read. “Undergraduates don’t get a lot of presentation opportunities, especially blackboard presentations,” says Zhao. Tristan Collins, left, received the Class of 1948 Career Development IMO Training 2007 Lemmas in Euclidean Geometry Yufei Zhao Lemmas inEuclideanGeometry 1 Yufei Zhao yufeiz@mit. All supplementary problems, Hidden independence and uniformity problems, Probability problems, and additional topics assignments from previous editions are based on files created by Prof. edu 1. (AM-GM) Let a 1; ;a n be positive real numbers. com/pm/ A. Annals of Mathematics 194 (2021), pp. Articles Cited by Public access Co-authors. You can find out lots more about me on Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. 22. OCW is open and available to the world and is a permanent MIT activity Prof. My research focuses on machine learning. MIT News Coverage *Zilin Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, Yufei Zhao. It is intended for students who enjoy solving challenging mathematical problems and who are Interview with Yufei Zhao Tou k Mansour Yufei Zhao received his Ph. I am a Ph. A34 (Mathematical Problem Solving, Putnam Seminar). Equiangular lines Joints Extension complexity Width of transitive sets. edu 18. Co-Authors: Eyal Ackerman, Mike Albertson, Boris Alexeev I recently graduated from the Massachusetts Institute of Technology (MIT) with a B. Fall 2019, MIT (Link to the most current version of the course). IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. Geometric and Functional Analysis, 31(5), 1160-1218. The dilation centered at G with ratio 2 takes M to A, and This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Your story matters. An independent set in a graph is a subset of vertices such that no two of them are joined by an edge. Sah, and Mehtaab Sawhney. Professor Yufei Zhao, who took 18. Let the tangent to at B and C meet at D. (AM-GM) Let a 1; ;a nbe positive real numbers. 218. 30. Let ABCD be a convex quadrilateral. Lines CA and DB meet at E; lines AN and CD meet at P; lines BN and CD meet This course is a graduate-level introduction to the probabilistic methods, a fundamental and powerful technique in combinatorics and theoretical computer science. 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. Equiangular lines with a fixed angle (with Zilin Jiang, Yuan Yao, Shengtong Zhang, and Yufei Zhao) Ann. S S + S S S This intuition helped to prove many results about MSTD sets. Address: 2005 Songhu Road, Shanghai, China. Course description. 95 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. Show that AC2 BD2 = AB2 CD2 + AD2 Yufei Zhao (赵宇飞) Massachusetts Institute of Technology Discrete Mathematics Office address：Room 102, SCMS Office tel： E-mail：yufeiz@mit. Zhao conducts research in discrete mathematics. Then AD coincides with a symmedian of ABC. DSpace@MIT. Notes from that course are available from its Yufei Zhao tenured at MIT. Time and Location: Please check the Google calendar below for the definitive schedule. When k= 1, 2p 1 +1 is divisible by 3 and greater than 9, so it must have at least 4 divisors. Meetings: Tuesdays and Thursdays 11am–noon in 2-135 Instructor: Yufei Zhao (see website for contact info) Course description. Fix an angle, in high dimensions, what is the maximum number of Trinity Training 2011 an 1 Yufei Zhao We use induction on k. This improves the previous Yufei Zhao yufeiz@mit. I think bagels are better than donuts. The Putnam Fellows for this year were Bohua Zhan and Yufei Zhao. Exponential improvements for superball packing upper bounds. He is literally scouting for new admitted students every year and training them together with old members. View Item . Fall 2018, MIT (Link to the most current version of the course). Lecture notes (MIT 18. “The Bipartite Swapping Trick on Many MIT Putnam competitors have prepared for the exam by participating in the first-year Putnam Seminar 18. Mathematics, MIT, 2010; S. 04021 Lecturer: Yufei Zhao Notes by: Andrew Lin Spring 2019 This is an edited transcript of the lectures of MIT’s Spring 2019 class 18. Zhao conducts research in discrete mathematics. Combinatorica 43 (2023), pp. Construction of the symmedian. Three of the next IMO Training 2008 Geometry Yufei Zhao Selected Geometry Problems from Recent IMO Shortlists 1. Yufei Zhao. Three of the next eleven highest ranking individuals were MIT students: Qingchun Ren, Colin Sandon, and Jacob Steinhardt. (The symmedian is the reflection of the median Fall 2019, MIT (Link to the most current version of the course). Notes by Yufei Zhao 27. 09462. Sc. “Yufei has made tremendous contributions in combinatorics with applications to computer science,” says Michael Sipser, Blog of Yufei Zhao, Associate Professor of Mathematics at MIT. Linear algebra tricks for the Putnam - MIT UMA Putnam Talk; Combinatorics. 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:. DSpace@MIT Home; MIT OpenCourseWare (MIT OCW) - Archived Zhao, Yufei. Let ABC be a triangle and its circumcircle. e. student in the mathematics department at MIT, advised by Henry Cohn and Yufei Zhao, and I teach each summer at Canada/USA Mathcamp. 226 (FALL 2022) – PROF. Yufei Zhao; Extending earlier work on equiangular lines, this paper studies the maximum number of unit vectors in \(\mathbb{R}^d\) whose pairwise inner products lie in some given \(L \subseteq MIT students score very highly annual Putnam Competition, taking 11 of 15 top spots in the grueling, prestigious challenge. Course description and policies IMO Training 2008 Polynomials Yufei Zhao 19. Location: Wilfrid Laurier University in Waterloo, Ontario Dates: June 27 to July 9, 2008 Summer camp participants, including local students IMO team members and trainers. Yufei's undergraduate mentees have already produced numerous high-quality results and published in prestigious venues. Looking at the coe cients Bound the size of the coe cients A. Stay Nikhil Agarwal, Andrew Lawrie, Yufei Zhao, and Daniel Harlow recently received 2019 Sloan Research Fellowships. (a) Let n be a positive integer. “Math competitions, such as the Putnam, have always been a male-dominated scene — which makes IMO Training 2007 Similarity Yufei Zhao Similarity Yufei Zhao July 12, 2007 yufeiz@mit. Tell us about your Trinity Training 2011 Power of a Point Yufei Zhao 4. Virginia Vassilevska Williams and delving into combinatorics with Prof. Four-peat: MIT students take first place in the 84th Putnam Math Competition Read it at MIT News. edu Office: 2-371 Class times: MWF 2-3, 2-151. A foundational result in additive combinatorics is Roth’s theorem, whic Fall 2023, MIT. 20. (Article in MIT News) 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. Title. Please share how this access benefits you. He is currently Assistant Professor of Mathematics at MIT. October 23: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. (Article in MIT News) Vishesh Jain, A. View Yufei Zhao’s profile on MIT won the 83rd William Putnam Mathematical Competition, sweeping the top five spots for third consecutive year. Middle matters less. Yufei Zhao Wins Future of Science Award. co_present (Image adapted by MIT OpenCourseWare from Supplementary Problems #3 (PDF). ps1 (a) Prove that A occupies at most 1/3 of the sphere in terms of surface area. Yufei Zhao (MIT) Eigenvalues of Random Graphs May 2012 3 / 46. edu 1 Bijections Basic examples 1. 226, Fall 2020) Probabilistic Methods in Combinatorics Yufei Zhao Massachusetts Institute of Technology yufeiz@mit. Sums and integrals Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. Quick links: [Lecture videos: MIT OCW, YouTube] [] []. Inventiones mathematicae, 221(2), 665-711. The notes have not been thoroughly checked for accuracy, espe-cially attributions of results. Zhao was named a Putnam Fellow in 2006, Instructor Interview. Bijections; Algebraic Techniques in Combinatorics - Spring 2019, MIT (Link to the most current version of the course). MIT School of Science. Let the line through M parallel to ‘ meet the circle 1 again at C and the circle 2 again at D. Only non-starred problems are considered for the calculations of Instructor: Yufei Zhao View the complete course: https://ocw. edu Lec 2, 9/12: Evan Chen evanchen@mit. Undergraduate Assistants (UA): MIT students dominate the Putnam Math Competition once again! 🍾 - Top five winners (Fellows) all come from MIT, including: - 3rd time Fellow for Experience: Massachusetts Institute of Yufei Zhao received his Ph. 1: 2023: New Lower Bounds and Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. I am excited by problems in extremal graph theory, discrete probability, and convex optimization. This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. My goal was to put together a cohesive introduction Hello! I'm Mingyang Deng, a first-year PhD student at MIT, where I'm fortunate to be advised by Prof. edu 1 Roots of unity 1. G(n;p) Largest eigenvalue ˇnp All other eigenvalues are O(p np). Let ABCbe a triangle and Γ its circumcircle. The joints problem is a classic problem in incidence geometry. Additional course material, Yufei Zhao (MIT) Joint work with Noga Alon (Princeton) and Jacob Fox (Stanford) June, 2018 1. We begin by summarizing some of the common approaches used in dealing with integer polynomials. Below, Professor Yufei Zhao describes various aspects of how he taught an earlier iteration of the course, 18. Singularity of discrete random matrices. March 01, 2024. Yufei Zhao; Departments Mathematics; Topics Mathematics. Yufei Zhao; Departments Mathematics; As Taught In Fall 2022 Level Graduate. ’ Gil Kalai, Hebrew University of Jerusalem and Reichman University ‘This is a beautiful treatment of extremal graph theory and additive combinatorics, focusing on the fruitful interplay between the two. of Math. “We hear a lot from MIT alumni that they wish they had received more training in communication skills at MIT. Location: C3 (week 1), C4 (weeks 2—8) Mathematical Institute, University of Oxford. The course focuses on methodology as well as Andrew Lawrie and Yufei Zhao were promoted to Associate Professor without Tenure. Publisher: Cambridge University Press ISBN: 9781009310949 Pages: 338 Content (The MIT Press Essential Knowledge series) Kate Eichhorn Current price: $15. Office hours by email appointment. Default locations are MIT Room 2-132 or Harvard Science Center Room 232 on Wednesdays, and MIT Room 2-139 on Thursdays. Note:In spectra plots, the matrices de-meaned and normalized. Richard Stanley in earlier versions of the course. Points X;Y, and Z lie on sides BC;CA IMO Training 2007 Lemmas in Euclidean Geometry Yufei Zhao Lemmas in Euclidean Geometry 1 Yufei Zhao yufeiz@mit. Advances in Mathematics, 365, 107056. in Mathematics (Course 18). Mathematics Professor Yufei Zhao, far right, stands with winners of the 78th annual William Lowell Putnam Mathematical Competition. A full list of my publications can be found on arXiv and Google Scholar. Inventiones Mathematicae, 221 (2020), 665–711. December 22, 2023. They are intended to serve as study Trinity Training 2011 an 1 Yufei Zhao (a)Show that 2 is a primitive root mod 3n for any n 1. Let the circumcircles of ABX and CDX meet again at O. 06914, 2023. A. Prof. edu 1 Warm up problems 1. edu Lec 5, 9/21: Morris Ang (Jie Jun) angm@mit. St. My policy is to not answer by email any math questions related to the class, due to time constraints and also 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. Let ‘ be the common tangent to 1 and 2 so that M is closer to ‘ than N is. MIT’s first-place finish earned $25,000 for the MIT math department, and each team member received $1,000. In my honest opinion, a simple man is responsible for MIT's success at the Putnam and his name is Yufei Zhao. Then AD coincides with a symmedian of 4ABC. Schedule and handouts Email: lguth@math. [Dropbox (schedule & homework PDFs)] [Canvas] Class meetings: Mondays and Wednesdays 1–2pm, room 2-132. Annals of The course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects. This course is based on another course taught by Larry Guth at MIT in Fall 2012. In this lecture, we will explore one such con guration. Singularity of discrete random IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. Quick links: [Problem set] Class meetings: Mondays and Wednesdays 2:30–4pm, room 4-153 Instructor: Prof. 1. Yufei Zhao Graders: Yibo Gao (lead), Milan Haiman, Anqi Li, Emails and Piazza. A. “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. Intuition Behind MSTD Sets Fringe is important. The number of independent sets in an irregular graph. Kaiming He. ISBN: 9781009310949. 217. edu. PROBLEM SET. Four from MIT Named 2019 Sloan Research Fellows. Testing triangle-free-ness [Rubin eld and Sudan ’96] [Goldreich, Goldwasser, Ron ’98] Goal: determine if an n-vertex graph istriangle-freeor -far from triangle free Zhao, Yufei. Britto-Pacumio in 1994 and Yinghui Wang in 2010. 217 Graph Theory and Additive Combinatorics, in the fall of 2019. Topics Fall 2017, MIT (Link to the most current version of the course). It is a prestigious award based on his research contribution to the field of combinatorics – as well as his mentorship, service and outreach. Yeah, Jeremy Hahn is more impressive. in mathematics at Princeton University in 2010. A typical question in incidence geometry concerns what kinds of configurations can Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. A34” in the subject line of your emails. Below, Professor Yufei Zhao describes various aspects of how he taught 18. Massachusetts Institute of Technology. Special office hours will be set up before homework due dates. Funct. Associate Professor of Mathematics. I’m happy to announce a new paper titled Joints tightened coauthored with Hung-Hsun Hans Yu, an undergraduate student at MIT. (b)Show that if gis an odd primitive root mod psuch that p2 - gp 1 1, then gis also a primitive root mod pn and 2pn for any n 1. A34 is a seminar intended for undergraduate students who enjoy solving challenging mathematical Yufei Zhao at MIT in Fall 2019. edu - Homepage. Equiangular lines N(d) = max # of lines in Rd with pairwise equal angles N(2) = 3 Papers by MIT combinatorialists—Fall 2023. From left are Junyao Peng In addition to having the 1st place team and 5 out of the 6 highest ranking individuals named Putnam Fellows, MIT had 5 of the next 9 top scorers, and 7 of the next 10. After k>1 groups have gone, every two students have gone together exactly once. Class meetings: Mondays and Wednesdays 2:30–4pm in 2-190 Lecturer: Yufei Zhao (see link for contact info) Office hours: Instead of scheduling regular office hours, the lecturer will be generally be available in the Math Common Room (2-290) after lectures to chat Instructor Insights. Then, we have a 1 + + a n n n p a 1 a n: Theorem 2. Biology; Brain and Cognitive Sciences; Chemistry; Fall 2022, MIT (Link to the most current version of the course). MIT wins Zhao wins Future of Science Award July 03, 2018. Selected publications IMO Training 2008 Polynomials Yufei Zhao 19. M Deng, J Tidor, Y Zhao. 211” in the subject line of your emails IMO Training 2008 Combinatorics Yufei Zhao Combinatorics July 6, 2008 Yufei Zhao yufeiz@mit. (USAMO 1976) The polynomials A(x);B(x);C(x);D(x) satisfy the equation Yufei Zhao MIT Based on joint work with David Conlon and Jacob Fox SIAM Conference on Discrete Mathematics D enes Konig Prize Lecture June 5, 2018. Canadian IMO Summer Training Camp 2008. edu Lec 3, 9/14: Yibo Gao gaoyibo@mit. 203-232. 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. Office hours: M 2:45-3:45pm & TR 2:30-3pm in 2-271. W 9/22 Lecture by Yufei Zhao. I am supported by a Hertz Graduate Fellowship and the NSF Graduate Research Fellowship Program. Advisor: Yufei Zhao (MIT) Research Interests: Extremal and probabilistic combinatorics. He has held postdoctoral and visiting positions at Stanford University, UC Berke-ley and Oxford. Let M be the midpoint of BC. The eigenvalues of the graph G are defined to be the eigenvalues of A(G). (Cauchy-Schwarz) Let a Lecturer: Yufei Zhao yufeiz@mit. Zhao is also a three-time Putnam Fellow. Under his coaching, MIT students have been Experience: Massachusetts Institute of Technology · Education: Massachusetts Institute of Technology · Location: Cambridge · 500+ connections on LinkedIn. A34 is a freshman advising seminar on mathematical problem solving. Cambridge University Press, 2023. Prove that the number 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. Faculty Features; Research; News; Watch; Attend Fall 2021, MIT, graduate level (Link to the most current version of the course). edu Visiting time:2019. 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. Introduction and linearity of expectations A1 Instructor Interview. We explore an intimate connection between Young tableaux and representa-tions of the symmetric group. edu/18-217F19 This course examines classical and modern developments in graph theory and add Virginia Vassilevska Williams MIT Verified email at mit. 729-743. edu We will use Z[x] to denote the ring of polynomials with integer coe cients. Joints of varieties (with Hung-Hsun Hans Yu and Yufei Zhao) Geom. Combinatorics. They need someone to teach combinatorics, keep the contest kids busy, and get some of them into research. edu Lec 4, 9/19: Ganesh Ajjanagadde gajjanag@mit. OCW: How did you approach designing and teaching this course? Yufei Zhao: This is the second iteration of a course I first taught in 2017. Michael F Sipser. 1 MIT OpenCourseWare is a web based publication of virtually all MIT course content. A34 (Mathematical Problem Solving, Putnam Seminar), taught by Zhao, who was a three-time Putnam Fellow when he was an undergraduate at MIT. Eigenvalues of random graphs Random d-regular graph G n;d Largest eigenvalue is d All other eigenvalues are O(p d). Prove that any complex zero of the polynomial satis es jzj 1. 18. Yufei Zhao Student, Massachusetts Institute of Technology 3 Ames St. in mathematics from the Massachusetts Institute of Technology (MIT) under the supervision of Jacob Fox. Points X;Y, and Z lie on sides BC;CA 1 Introduction Paul Erdős (1913–1996) is considered the father of the probabilistic method. Contents 1 Introduction 2 Before recently joining Stanford, I enjoyed the hospitality of the MIT Department of Mathematics. My advisor was Benny Sudakov. October 28: Charles River Lectures on Probability Theory and Related Topics in E51 MIT Tang Center. Yufei Zhao Massachusetts Institute of Technology Verified email at mit. W 9/29 Lecture by Daniel Zhu. Instructor: Prof. Teaching assistants: Pro Pakawut Jiradilok and Morris Jie Jun Ang Please include “18. Equiangular lines with a fixed angle. Suppose that 2a + 1 has at least 4k 1 divisors. 99 Publish Date: November 2nd, 2023. Spherical two-distance sets and eigenvalues of signed graphs. There were also 52 MIT students in the 201-500 finishers. arXiv:1805. (Cauchy-Schwarz) Let a Winter Camp 2008 Inequalities Yufei Zhao 1 a Tagged: Yufei Zhao. Discrete geometry. Background on connections between analysis and IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. The notes were written by the students of the class based on the lectures, and edited with the help of the professor. arXiv preprint arXiv:2307. 13Mb) Yufei Zhao (MIT) MSTD Sets and Beyond 1/14/2010 6 / 12. edu An important skill of an olympiad geometer is being able to recognize known con gurations. Indeed, many geometry problems are built on a few common themes. October 30: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. , P a2A 1=a, must contain arbitrarily long APs. Class meetings: Mondays and Wednesdays 1–2pm, room 2-132 Instructor: Prof. He is currently Assistant Professor of Mathematics Prof. Massachusetts Institute of Technology Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue MIT OpenCourseWare is a web based publication of virtually all MIT course content. Graph Theory and Additive Combinatorics: Exploring Structure and Randomness. Yufei received his dual SB degrees in Mathematics and Computer Science from MIT in 2010, an MASt in Yufei Zhao is a combinatorist who emigrated from China to Canada and then to the US. Current price: $69. “I congratulate all the students for their performance in the Putnam Competition. Class meetings: Mondays and Wednesdays 1–2pm in 4-149 Instructor: Yufei Zhao (see link for contact info) Please include “18. October 25: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. Instructor: Yufei Zhao. 226 Probabilistic Methods in Combinatorics. " In this note, we will mainly focus on how to use incidence Fall 2021, MIT (Link to the most current version of the course) Class meetings: Mondays and Wednesdays 1–2pm, room 2-147. MIT Open Access Articles The Bipartite Swapping Trick on Graph Homomorphisms The MIT Faculty has made this article openly available. ) Download Zhao, Yufei. (IMO 2000) Two circles 1 and 2 intersect at M and N. 12. Fall 2018, MIT. Like Urschel he fits into their business model / development strategy. I am a PhD student in the Department of Mathematics at MIT. Grading. This conjecture is widely believed to be true, but it has yet to be proved even in the case of 3-term APs2. Additional course material, Yufei Zhao Extremal, probabilistic, and additive combinatorics; Instructors & Postdocs. B. Verified email at mit. Mathematics, Emeritus. Prove that triangles OAB and OCD are similar. IMO Training 2008 Polynomials Yufei Zhao Polynomials July 2, 2008 Yufei Zhao yufeiz@mit. He shares his personal and academic journey, his love of math, and his advice to students at MIT. Yufei Zhao Yufei Zhao himself is a major player in modern research in both these areas and his presentation is a tour de force. Well deserved, Bravo! 7 months ago # QUOTE 9 Good 2 No Giod! Economist Data. Time: Tuesday 10—11. YUFEI ZHAO ABSTRACT. Let P(x) = a 0 + a 1x+ + a nxn, where 0 <a 0 a 1 a n are real numbers. Let a= p 1 p k 1 and b= p k. pdf. This technique is often called \double counting. He received his SB in Mathematics and Computer Science from MIT in 2010, his Masters of Advanced Study in Mathematics from Cambridge in 2011, and his PhD in Mathematics from MIT in 2015. By the lemma, A;Y;D are collinear. He solved an open problem in graph theory, simplified the proof of the Green-Tao “In high dimensions, things really get interesting, and the possibilities can seem limitless,” says Yufei Zhao, assistant professor of mathematics. “Our students' outstanding performance on the Putnam is a testament to their dedication and Prof. Hepublishedaround1,500papersduringhislifetime, andhadmorethan500 Winter Camp 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. Yufei Zhao • Explored Ruzsa’s conjecture; improved bounds and established new links to arithmetic Ramsey problems. Topics Selected publications. Ren and Zhao also earned the Putnam Fellow distinction, which carries a $2,500 prize, for finishing in the top five. Sah, Mehtaab Sawhney, David Stoner, and Yufei Zhao. Back to main | Mehtaab Sawhney wins Clay Research Fellowship 1/25/2024 Papers by MIT combinatorialists—Fall 2023 12/22/2023 Summaries of recent papers by students and postdocs 2 DAVID CONLON, JACOB FOX, AND YUFEI ZHAO with divergent harmonic sum, i. " In this note, we will mainly focus on how to use incidence 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. Donner Professor of Mathematics. Ph. Mathematics with Distinction, Cambridge, 2011; S. (2006/G2) Let ABCD be a trapezoid with parallel sides AB > CD. Notify us about copyright concerns. Yufei Zhao is Assistant Professor of Mathematics at the Massachusetts Institute of Technology. Zhao's main research area is combinatorics, specifically the extremal, probabilistic, and additive flavors. Economist Koopmans. Let ‘ touch 1 at A and 2 at B. Supervised Program for Alignment Research Mar2023–Aug2023 Z ilin Jiang, J onathan Tidor, Y uan Yao, S hengtong Zhang, Y ufei Zhao. Let the tangent to Γ at Band Cmeet at D. Journal of Combinatorial Theory, Series B, 138 (2019), 172-195. Each section focuses on a different technique, along with examples of applications. 7 months ago # QUOTE 4 Good 13 No Giod! Economist Scholes. ps1? (b) Prove an upper bound smaller than 1/3 (give your best bound). mit. IMO Training 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. The course focuses on methodology as well as MOP 2007 Black Group Integer Polynomials Yufei Zhao Integer Polynomials June 29, 2007 Yufei Zhao yufeiz@mit. 19-12. MIT has won the Putnam competition six times since its inception in 1938, with the most recent victories in 2003 and 2004. wns tfpfx lowdv gchgok mnpphcz qdch tzb xewaba alrfa ajbhlt