Yufei zhao mit. 226 Probabilistic Methods in Combinatorics.

Yufei zhao mit The joints problem is a classic problem in incidence geometry. arXiv preprint arXiv:2307. DownloadThis package contains the same content as the online version of the course, except for the audio/video materials. Under his coaching, MIT students have been Experience: Massachusetts Institute of Technology · Education: Massachusetts Institute of Technology · Location: Cambridge · 500+ connections on LinkedIn. Primary DLC. My research focuses on machine learning. MIT’s first-place finish earned $25,000 for the MIT math department, and each team member received $1,000. This year’s cohort brings MIT’s total to nearly 300 fellows — more than any single institution in the history of the fellowships. Talks take place at MIT and Harvard. PROBLEM SET. edu Visiting time:2019. Journal of Combinatorial Theory, Series B, 138 (2019), 172-195. 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. 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. “Our students' outstanding performance on the Putnam is a testament to their dedication and Prof. I completed my Ph. Then, we have a 1 + + a n n n p a 1 a n: Theorem 2. Course description. 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. student in the mathematics department at MIT, advised by Henry Cohn and Yufei Zhao, and I teach each summer at Canada/USA Mathcamp. “Undergraduates don’t get a lot of presentation opportunities, especially blackboard presentations,” says Zhao. 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 . Mathematics, MIT, 2015 (Advisor: Jacob Fox) M. ’ MOP 2007 Black Group Counting in Two Ways Yufei Zhao Counting in Two Ways Incidence Matrices June 26, 2007 Yufei Zhao yufeiz@mit. 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. Virginia Vassilevska Williams and delving into combinatorics with Prof. Three of the next eleven highest ranking individuals were MIT students: Qingchun Ren, Colin Sandon, and Jacob Steinhardt. edu A Taste of Algebraic Combinatorics Problem: (St. G(n;p) Largest eigenvalue ˇnp All other eigenvalues are O(p np). Supervised Program for Alignment Research Mar2023–Aug2023 Z ilin Jiang, J onathan Tidor, Y uan Yao, S hengtong Zhang, Y ufei Zhao. 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. Combinatorica 43 (2023), pp. edu 1. Intuition Behind MSTD Sets Fringe is important. MIT Room: 2-271 (617) 253-4380. (Cauchy-Schwarz) Let a Lecturer: Yufei Zhao yufeiz@mit. Quick links: [Lecture videos: MIT OCW, YouTube] [] []. 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. 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. I am excited by problems in extremal graph theory, discrete probability, and convex optimization. Prof. A34 (Mathematical Problem Solving, Putnam Seminar). A reverse Sidorenko inequality. 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. Lecture notes (MIT 18. In this lecture, we will explore one such con guration. Funct. I earned my undergraduate complexity under the guidance of Prof. ) Download Zhao, Yufei. Primarily based on problem sets. (17. He is literally scouting for new admitted students every year and training them together with old members. IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. In my honest opinion, a simple man is responsible for MIT's success at the Putnam and his name is Yufei Zhao. edu Office: 2-371 Class times: MWF 2-3, 2-151. Notify us about copyright concerns. (AM-GM) Let a 1; ;a n be positive real numbers. 194 (2021), 729–743. 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. Additional course material, Yufei Zhao Extremal, probabilistic, and additive combinatorics; Instructors & Postdocs. Quick links: [Problem set] Class meetings: Mondays and Wednesdays 2:30–4pm, room 4-153 Instructor: Prof. Left to right: Coach Yufei Zhao poses with winners Ashwin Sah, Shengtong Zhang, Yuan Yao, Acknowledgements. 1. Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. in mathematics from the Massachusetts Institute of Technology (MIT) under the supervision of Jacob Fox. Computer Science and Engineering, Yufei Zhao joined the mathematics faculty as Assistant Professor in July 2017. Zhao is also a three-time Putnam Fellow. edu. Additional course material, Yufei Zhao (MIT) Joint work with Noga Alon (Princeton) and Jacob Fox (Stanford) June, 2018 1. Sah, and Mehtaab Sawhney. 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. 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. 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. Current price: $69. St. An independent set in a graph is a subset of vertices such that no two of them are joined by an edge. edu/18-217F19 This course examines classical and modern developments in graph theory and add Virginia Vassilevska Williams MIT Verified email at mit. (Article in MIT News) Vishesh Jain, A. The course also introduces students to current research topics and open problems. MIT Open Access Articles The Bipartite Swapping Trick on Graph Homomorphisms The MIT Faculty has made this article openly available. Mathematics, MIT, 2010; S. 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. . 99 Publish Date: November 2nd, 2023. Suppose that 2a + 1 has at least 4k 1 divisors. This course is based on another course taught by Larry Guth at MIT in Fall 2012. 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. I think bagels are better than donuts. Indeed, many geometry problems are built on a few common themes. 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. edu Nitya Mani. Class meetings: Mondays and Wednesdays 1–2pm in 4-149 Instructor: Yufei Zhao (see link for contact info) Please include “18. Britto-Pacumio in 1994 and Yinghui Wang in 2010. Sah, Mehtaab Sawhney, David Stoner, and Yufei Zhao. OCW is open and available to the world and is a permanent MIT activity Prof. " 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. “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. My papers are listed below by topic. Department of Mathematics. Paper underreviewatMPCPS. Donner Yufei Zhao, an assistant professor of mathematics at MIT, is honored for his research in discrete mathematics, teaching, service, and outreach. 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. Mathematics with Distinction, Cambridge, 2011; S. Let M be the midpoint of BC. Petersburg) Students in a school go for ice cream in groups of at least two. Location: C3 (week 1), C4 (weeks 2—8) Mathematical Institute, University of Oxford. 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. (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. Canadian IMO Summer Training Camp 2008. Time and Location: Please check the Google calendar below for the definitive schedule. Below, Professor Yufei Zhao describes various aspects of how he taught 18. Research. 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. 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. Like Urschel he fits into their business model / development strategy. 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. Linear algebra tricks for the Putnam - MIT UMA Putnam Talk; Combinatorics. Discrete geometry. Selected publications IMO Training 2008 Polynomials Yufei Zhao 19. Hepublishedaround1,500papersduringhislifetime, andhadmorethan500 Winter Camp 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. Let the circumcircles of ABX and CDX meet again at O. 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. Singularity of discrete random IMO Training 2008 Circles Yufei Zhao Circles 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. Let the tangent to at B and C meet at D. Citation: Zhao, Yufei. Fall 2018, MIT. Yufei Zhao; Administrative Assistant: Yufei An, yfa@mit. MIT wins Zhao wins Future of Science Award July 03, 2018. 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. edu Lec 5, 9/21: Morris Ang (Jie Jun) angm@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. 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. Other than those listed below, all problem sets were created by anonymous guest lecturers. Yufei Zhao Massachusetts Institute of Technology Verified email at mit. The course focuses on methodology as well as Andrew Lawrie and Yufei Zhao were promoted to Associate Professor without Tenure. Instructor: Prof. This conjecture is widely believed to be true, but it has yet to be proved even in the case of 3-term APs2. Sign up to receive news and updates from MIT Industrial Liaison Program Sign up. Default locations are MIT Room 2-132 or Harvard Science Center Room 232 on Wednesdays, and MIT Room 2-139 on Thursdays. in mathematics at Princeton University in 2010. "Abstract:Sol At MIT there is literally a course that prepares you for Putnam - literally search for MIT Putnam seminar. Two other MIT Elizabeth Putnam Prize winners are Ruth A. View Item . 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. Equiangular lines with a fixed angle (with Zilin Jiang, Yuan Yao, Shengtong Zhang, and Yufei Zhao) Ann. Economist Stiglitz. My advisor was Benny Sudakov. Prove that any complex zero of the polynomial satis es jzj 1. edu 1 Roots of unity 1. (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. DSpace@MIT Home; MIT OpenCourseWare (MIT OCW) - Archived Zhao, Yufei. of Math. pdf. 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:. Only non-starred problems are considered for the calculations of Instructor: Yufei Zhao View the complete course: https://ocw. Sums and integrals Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. By the lemma, A;Y;D are collinear. Massachusetts Institute of Technology. Zilin Jiang, Jonathan Tidor, me, Yuan Yao, Shengtong Zhang. YUFEI ZHAO ABSTRACT. ’ 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. 13Mb) Yufei Zhao (MIT) MSTD Sets and Beyond 1/14/2010 6 / 12. 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. 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. 226 (FALL 2022) – PROF. YUFEI ZHAO PROBLEM SET A. Michael F Sipser. 226, Fall 2020) Probabilistic Methods in Combinatorics Yufei Zhao Massachusetts Institute of Technology yufeiz@mit. 217 Graph Theory and Additive Combinatorics, in the fall of 2019. Read. Schedule and handouts Email: lguth@math. 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. Equiangular lines N(d) = max # of lines in Rd with pairwise equal angles N(2) = 3 Papers by MIT combinatorialists—Fall 2023. 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. Yufei Zhao is Assistant Professor of Mathematics at the Massachusetts Institute of Technology. You can find out lots more about me on Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. A34” in the subject line of your emails. 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. M 9/27 Discussion — Presentations. He has held postdoctoral and visiting positions at Stanford University, UC Berke-ley and Oxford. 7 months ago # QUOTE 7 Good 4 No Giod! Economist MIT OpenCourseWare is a web based publication of virtually all MIT course content. Topics Selected publications. MIT; Supervised by Prof. e. , P a2A 1=a, must contain arbitrarily long APs. edu Lec 4, 9/19: Ganesh Ajjanagadde gajjanag@mit. (Cauchy-Schwarz) Let a Winter Camp 2008 Inequalities Yufei Zhao 1 a Tagged: Yufei Zhao. Blog. ISBN: 9781009310949. edu http://yufeizhao. arXiv:1809. After k>1 groups have gone, every two students have gone together exactly once. Address: 2005 Songhu Road, Shanghai, China. Sc. Let AB and CD be two segments, and let lines AC and BD meet at X. edu Editor-in-chief: Gwen McKinley gweneth@mit. Y Zhao. (a) Let n be a positive integer. 1 MIT OpenCourseWare is a web based publication of virtually all MIT course content. December 22, 2023. 211 Combinatorial Analysis. Instructor: Yufei Zhao. When k= 1, 2p 1 +1 is divisible by 3 and greater than 9, so it must have at least 4 divisors. 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. In Fall 2017, MIT (Link to the most current version of the course). 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. Yeah, Jeremy Hahn is more impressive. Contents 1 Introduction 2 Before recently joining Stanford, I enjoyed the hospitality of the MIT Department of Mathematics. 226 Probabilistic Methods in Combinatorics. “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. Graph Theory and Additive Combinatorics: Exploring Structure and Randomness. 09462. With high probability, most of the middle sums and di erences will be present. Fall 2019, MIT (Link to the most current version of the course). Meetings: Tuesdays and Thursdays 11am–noon in 2-135 Instructor: Yufei Zhao (see website for contact info) Course description. D. Exponential improvements for superball packing upper bounds. 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). Geometric and Functional Analysis, 31(5), 1160-1218. (The symmedian is the reflection of the median Fall 2019, MIT (Link to the most current version of the course). Kaiming He. Let ABCD be a convex quadrilateral. Teaching assistants: Pro Pakawut Jiradilok and Morris Jie Jun Ang Please include “18. 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. Office hours: M 2:45-3:45pm & TR 2:30-3pm in 2-271. edu A large number of combinatorics problems involve looking at a quantity in at least two di erent ways. MIT could do better. 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. Three of the next IMO Training 2008 Geometry Yufei Zhao Selected Geometry Problems from Recent IMO Shortlists 1. MIT has won the Putnam competition six times since its inception in 1938, with the most recent victories in 2003 and 2004. 211” in the subject line of your emails IMO Training 2008 Combinatorics Yufei Zhao Combinatorics July 6, 2008 Yufei Zhao yufeiz@mit. Points X;Y, and Z lie on sides BC;CA Yufei Zhao tenured at MIT. 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. A34 is a freshman advising seminar on mathematical problem solving. I am a Ph. Associate Professor of Mathematics. Points X;Y, and Z lie on sides BC;CA 1 Introduction Paul Erdős (1913–1996) is considered the father of the probabilistic method. 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. Bijections; Algebraic Techniques in Combinatorics - Spring 2019, MIT (Link to the most current version of the course). 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. edu 1 Classical Theorems Theorem 1. This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. Winter Camp 2009 Cyclic Quadrilaterals Yufei Zhao Cyclic Quadrilaterals | The Big Picture Yufei Zhao yufeiz@mit. This improves the previous Yufei Zhao yufeiz@mit. A foundational result in additive combinatorics is Roth’s theorem, whic Fall 2023, MIT. 2. Let ABCbe a triangle and Γ its circumcircle. Let ‘ touch 1 at A and 2 at B. Fall 2018, 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. 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. Professor Yufei Zhao, who took 18. Then AD coincides with a symmedian of 4ABC. October 28: Charles River Lectures on Probability Theory and Related Topics in E51 MIT Tang Center. Yufei Zhao (MIT) Eigenvalues of Random Graphs May 2012 3 / 46. 218: The Probabilistic Method in Combinatorics, taught by Professor Yufei Zhao. DSpace@MIT. , Cambridge MA, 02142, USA yufeiz@mit. 218. Please share how this access benefits you. The Putnam Fellows for this year were Bohua Zhan and Yufei Zhao. A. Yufei Zhao Wins Future of Science Award. Combinatorics. Richard Stanley in earlier versions of the course. 18. The course examines classical and modern developments in graph theory and additive combinatorics, with a focus PROBABILISTIC METHODS IN COMBINATORICS MIT 18. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. 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. Let a= p 1 p k 1 and b= p k. (2006/G2) Let ABCD be a trapezoid with parallel sides AB > CD. Andy works on understanding the asymptotic dynamics of solutions to partial differential equations. " 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. Let the line through M parallel to ‘ meet the circle 1 again at C and the circle 2 again at D. Yufei's undergraduate mentees have already produced numerous high-quality results and published in prestigious venues. Donner Professor of Mathematics. A34 is a seminar intended for undergraduate students who enjoy solving challenging mathematical Yufei Zhao at MIT in Fall 2019. Construction of the symmedian. Yufei Zhao Student, Massachusetts Institute of Technology 3 Ames St. 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. But they aren’t limitless, according to Zhao and his team of MIT Yufei Zhao. I am fortunate to be advised by Pablo Parrilo and Yufei Zhao. Cambridge University Press, 2023. 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. Zhao conducts research in discrete mathematics. W 9/22 Lecture by Yufei Zhao. October 23: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. The notes were written by the students of the class based on the lectures, and edited with the help of the professor. Ph. (AM-GM) Let a 1; ;a nbe positive real numbers. The notes have not been thoroughly checked for accuracy, espe-cially attributions of results. Zhao was named a Putnam Fellow in 2006, Instructor Interview. Special office hours will be set up before homework due dates. Inventiones Mathematicae, 221 (2020), 665–711. Mathematics, Emeritus. 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. Advisor: Yufei Zhao (MIT) Research Interests: Extremal and probabilistic combinatorics. 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. Yufei Zhao • Explored Ruzsa’s conjecture; improved bounds and established new links to arithmetic Ramsey problems. Course description and policies IMO Training 2008 Polynomials Yufei Zhao 19. Class time: Tuesdays and Thursdays 9:30—11am Location: 66-144 (Room change! Lecturer: Yufei Zhao (see website for contact info). Articles Cited by Public access Co-authors. Your story matters. edu 1 Warm up problems 1. Yufei works on problems in extremal combinatorics, spectral graph theory, and discrete geometry. Equiangular lines with a fixed angle. Co-Authors: Eyal Ackerman, Mike Albertson, Boris Alexeev I recently graduated from the Massachusetts Institute of Technology (MIT) with a B. Equiangular lines Joints Extension complexity Width of transitive sets. 14. Class meetings: Mondays and Wednesdays 1–2pm, room 2-132 Instructor: Prof. (IMO 2000) Two circles 1 and 2 intersect at M and N. com/pm/ A. MIT News Coverage *Zilin Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, Yufei Zhao. Postcode: Yufei Zhao is a Junior Research Fellow in Mathematics at New College, Oxford. mit. 06914, 2023. Let ABC be a triangle and its circumcircle. “I congratulate all the students for their performance in the Putnam Competition. 217. 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. Notes by Yufei Zhao 27. IMO Training 2008 Inequalities Yufei Zhao Inequalities Yufei Zhao yufeiz@mit. in Mathematics (Course 18). 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. IMO Training 2008 Polynomials Yufei Zhao Polynomials July 2, 2008 Yufei Zhao yufeiz@mit. Topics Fall 2017, MIT (Link to the most current version of the course). Learning Resource Types assignment Problem Sets. Due: Hidden independence and uniformity & SS3. March 01, 2024. Office hours by email appointment. The eigenvalues of the graph G are defined to be the eigenvalues of A(G). Four from MIT Named 2019 Sloan Research Fellows. Notes from that course are available from its Yufei Zhao tenured at MIT. 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. Below, Professor Yufei Zhao describes various aspects of how he taught an earlier iteration of the course, 18. edu Lec 1, 9/7: Yufei Zhao yufeiz@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. A34 (Mathematical Problem Solving, Putnam Seminar), taught by Zhao, who was a three-time Putnam Fellow when he was an undergraduate at MIT. Note:In spectra plots, the matrices de-meaned and normalized. ps1? (b) Prove an upper bound smaller than 1/3 (give your best bound). 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. (Miquel’s theorem) Let ABC be a triangle. co_present (Image adapted by MIT OpenCourseWare from Supplementary Problems #3 (PDF). Then AD coincides with a symmedian of ABC. A. Prove that triangles OAB and OCD are similar. October 25: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. [Dropbox (schedule & homework PDFs)] [Canvas] Class meetings: Mondays and Wednesdays 1–2pm, room 2-132. Yufei Zhao; Departments Mathematics; As Taught In Fall 2022 Level Graduate. (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. Let pbe a prime. edu An important skill of an olympiad geometer is being able to recognize known con gurations. We begin by summarizing some of the common approaches used in dealing with integer polynomials. 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. Mathematics Professor Yufei Zhao, far right, stands with winners of the 78th annual William Lowell Putnam Mathematical Competition. They need someone to teach combinatorics, keep the contest kids busy, and get some of them into research. Well deserved, Bravo! 7 months ago # QUOTE 9 Good 2 No Giod! Economist Data. Annals of Mathematics 194 (2021), pp. 30. Let the tangent to Γ at Band Cmeet at D. Spherical two-distance sets and eigenvalues of signed graphs. A full list of my publications can be found on arXiv and Google Scholar. “That was a very nice solution,” math professor Yufei Zhao told the class. Yufei Zhao Graders: Yibo Gao (lead), Milan Haiman, Anqi Li, Emails and Piazza. Ren and Zhao also earned the Putnam Fellow distinction, which carries a $2,500 prize, for finishing in the top five. He is currently Assistant Professor of Mathematics at MIT. Faculty Features; Research; News; Watch; Attend Fall 2021, MIT, graduate level (Link to the most current version of the course). Yufei Zhao. 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. He shares his personal and academic journey, his love of math, and his advice to students at MIT. W 9/29 Lecture by Daniel Zhu. S S + S S S This intuition helped to prove many results about MSTD sets. home cv research blog. 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. 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. Publisher: Cambridge University Press ISBN: 9781009310949 Pages: 338 Content (The MIT Press Essential Knowledge series) Kate Eichhorn Current price: $15. Stay Nikhil Agarwal, Andrew Lawrie, Yufei Zhao, and Daniel Harlow recently received 2019 Sloan Research Fellowships. Middle matters less. B. His work is unimpressive. Fix an angle, in high dimensions, what is the maximum number of Trinity Training 2011 an 1 Yufei Zhao We use induction on k. Class meetings: Tuesdays and Thursdays 1–2:30pm in 2-135 Lecturer: Yufei Zhao (see website for contact info). 20. The number of independent sets in an irregular graph. Looking at the coe cients Bound the size of the coe cients A. October 30: Yufei Zhao, A quasi-polynomial bound for the Freiman-Ruzsa theorem. Thue's proof part III Introduction to the Kakeya problem 29. 19-12. ps1 (a) Prove that A occupies at most 1/3 of the sphere in terms of surface area. M Deng, J Tidor, Y Zhao. “We hear a lot from MIT alumni that they wish they had received more training in communication skills at MIT. Each section focuses on a different technique, along with examples of applications. arXiv:1805. He is currently Assistant Professor of Mathematics Prof. 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. We explore an intimate connection between Young tableaux and representa-tions of the symmetric group. This technique is often called \double counting. Tell us about your Trinity Training 2011 Power of a Point Yufei Zhao 4. 729-743. Yufei Zhao; Departments Mathematics; Topics Mathematics. Advances in Mathematics, 365, 107056. There were also 52 MIT students in the 201-500 finishers. Title. A typical question in incidence geometry concerns what kinds of configurations can Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. 203-232. Let ‘ be the common tangent to 1 and 2 so that M is closer to ‘ than N is. This course was previously numbered 18. (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. Yufei Zhao; Departments Mathematics; As Taught In Fall 2018 Level Undergraduate. Joints of varieties (with Hung-Hsun Hans Yu and Yufei Zhao) Geom. Zhao conducts research in discrete mathematics. Eigenvalues of random graphs Random d-regular graph G n;d Largest eigenvalue is d All other eigenvalues are O(p d). A34 is a first-year undergraduate seminar on mathematical problem solving. edu - Homepage. Time: Tuesday 10—11. Hung-Hsun Hans Yu. View Yufei Zhao’s profile on MIT won the 83rd William Putnam Mathematical Competition, sweeping the top five spots for third consecutive year. Zhao's main research area is combinatorics, specifically the extremal, probabilistic, and additive flavors. 1: 2023: New Lower Bounds and Winter Camp 2008 Combinatorics Yufei Zhao Combinatorics Yufei Zhao yufeiz@mit. edu Lec 2, 9/12: Evan Chen evanchen@mit. Let r = (r. Introduction and linearity of expectations A1 Instructor Interview. I am a PhD student in the Department of Mathematics at MIT. edu We will use Z[x] to denote the ring of polynomials with integer coe cients. Thue's proof part II: polynomials of two variables 28. Yufei Zhao Yufei Zhao himself is a major player in modern research in both these areas and his presentation is a tour de force. MIT School of Science. 12. INTRODUCTION A. Link to Canvas. MOP 2007 Black Group Integer Polynomials Yufei Zhao Integer Polynomials June 29, 2007 Yufei Zhao yufeiz@mit. Singularity of discrete random matrices. edu 1 Bijections Basic examples 1. 7 months ago # QUOTE 4 Good 13 No Giod! Economist Scholes. I am supported by a Hertz Graduate Fellowship and the NSF Graduate Research Fellowship Program. Yufei Zhao MIT CanaDAM 2021. Grading. Economist Koopmans. I’m happy to announce a new paper titled Joints tightened coauthored with Hung-Hsun Hans Yu, an undergraduate student at MIT. Inventiones mathematicae, 221(2), 665-711. 22. “The Bipartite Swapping Trick on Many MIT Putnam competitors have prepared for the exam by participating in the first-year Putnam Seminar 18. Then MI is a midline of triangle XYD, so IM and YD are parallel. Verified email at mit. Biology; Brain and Cognitive Sciences; Chemistry; Fall 2022, MIT (Link to the most current version of the course). edu Lec 3, 9/14: Yibo Gao gaoyibo@mit. In this paper, we determine the tight constant in the joints problem. Background on connections between analysis and IMO Training 2008 Circles Yufei Zhao Circles Yufei Zhao yufeiz@mit. “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. Four-peat: MIT students take first place in the 84th Putnam Math Competition Read it at MIT News. Let P(x) = a 0 + a 1x+ + a nxn, where 0 <a 0 a 1 a n are real numbers. 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. edu 18. roy mlguhes tjn zrsbo tqwrh gqd jwzav pyvl nigi ajf