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. Independence problem solved through collaboration mit news. This is the second iteration of a course i first taught two years ago. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including szemer\edis regularity lemma and its use, shelahs extension of the halesjewett theorem, the precise nature of the phase transition. Imo training 2010 projective geometry alexander remorov poles and polars given a circle. Siam journal on discrete mathematics siam society for. Yufei zhao teaching graph theory and additive combinatorics. In 2, the authors systematically study the local structure of differentiable graphon parameters. We provide an upper bound to the number of graph homomorphisms from g to h, where h is a fixed graph with certain properties, and g varies over all nvertex, dregular graphs. If you would like to contribute, please donate online using credit card or bank transfer or mail.
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 sciences future of. Department of mathematics yufei zhao joined the mathematics faculty as assistant professor in july 2017. Zhao, the number of independent sets in a regular graph, combin probab comput volume 19 2010, pp. His focus is on combinatorics, discrete mathematics, and graph theory. He received his sb in mathematics and computer science from mit in 2010, his masters of advanced study in mathematics. The illustrations of geometry problems were done in wingclc, a program created by prof. S997, graph theory and additive combinatorics, fall 2017, yufei zhao. Yufei zhao graduated in 2010, received his phd in 2015, and is now the class of 1956 career development assistant professor at mit. The earliest result in extremal graph theory is usually credited to mantel, who proved, in 1907, that a graph on vertices with no triangles contains at most edges, where the maximum is achieved for a complete bipartite graph with half of the vertices on one side and half on the other side. I wanted to create a set of notes, eventually turning into a new textbook, that.
David conlons research while affiliated with university of oxford and other places. May 03, 2018 in the exponential random graph model, one samples an nvertex random graph g with probability proportional to expfg, where fg is some graph parameter. I didnt set out to study highdimensional footballs for their own sake. Join facebook to connect with yufei yufei zhao and others you may know. We prove our main result via a new insight in spectral graph theory, namely. Journal of combinatorial theory, series b vol 8, pages. The earliest result in extremal graph theory is usually credited to mantel, who proved, in 1907. Equiangular lines with a fixed angle with zilin jiang, jonathan tidor, yuan yao, and shengtong zhang advances in mathematics 319 2017, 3347. Handbook of graph theory discrete mathematics and its. Extremal and ramsey results on graph blowups, 2019.
Online books by topic number theory by justin stevens number theory by david santos geometry revisited by h. Yufei zhao large deviations and exponential random graphs. The celebrated greentao theorem states that there are arbitrarily long arithmetic progressions in the primes. Acknowledgement much of the material in these notes is from the books graph theory by reinhard diestel, introductiontographtheory. Much of the material in these notes is from the books graph theory by reinhard diestel, intro ductiontographtheory bydouglaswest,andproofsfromthebook bymartinaignerandgunter ziegler. Results may not be complete and may include mistakes. Yufei returned to mit for his phd in 2011 to study extremal, probabilistic and additive combinatorics which involved understanding how to use graph theory to better comprehend prime numbers and the. The competition was founded in 1927 by elizabeth lowell putnam in memory of her husband william lowell putnam, who was an advocate of intercollegiate intellectual competition. William lowell putnam mathematical competition wikipedia. Yufei zhao is a junior research fellow in mathematics at new college, oxford. Yufei zhao simons institute for the theory of computing.
The william lowell putnam mathematical competition, often abbreviated to putnam competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher. Yufei zhao joined the mathematics faculty as assistant professor in july 2017. Dec 16, 2019 conference on graph theory and its applications. Yufei zhao massachusetts institute of technology verified email at mit. Graph theory and additive combinatorics mathematics mit.
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. Yufei zhao, sets characterized by missing sums and differences, journal of number theory, 11 2011 210724. Journal of combinatorial theory, series b vol 8, pages 1. Imc 2002 two hundred students participated in a mathematical contest. This is the homepage for a textbook that i plan to write. On derivatives of graphon parameters sciencedirect. There are numerous instances when tutte has found a beautiful result in a. See the complete profile on linkedin and discover yufeis. The exam has been offered annually since 1938 and is administered by the mathematical association of america. Gross is the coauthor of several books and the inventor of the voltage graph, a construct widely used in topological graph theory and other areas. Limits, sparse random graph models, and power law distributions.
His current research interests include the genus distribution of graphs, computer graphics, and knot theory. A recipient of numerous awards and research grants, dr. David conlons 103 research works with 1,328 citations and 5,738 reads, including. Ams transactions of the american mathematical society. Everyday low prices and free delivery on eligible orders.
Limits, sparse random graph models, and power law distributions authors. Buy sparse optimization theory and methods 1 by zhao, yunbin isbn. View yufei zhaos profile on linkedin, the worlds largest professional community. Greitzer geometry unbound by kiran kedlaya combinatorics by. Understanding the limitations of the regularity lemmain the regularity partition, how does the number of parts depend on the regularity parameter. Tufte this book is formatted using the tuftebook class. David conlons research works university of oxford, oxford. Sep 07, 2012 graph regularity is an active research area. The post is based on a talk i gave earlier today at a graduate student. Instructor insights graph theory and additive combinatorics. Graph theory and additive combinatorics, taught by prof. Aug 14, 2018 buy sparse optimization theory and methods 1 by zhao, yunbin isbn.
Zhao da yuan is the author of practical qin na part two 5. He worked on a research problem in graph theory concerning. Transactions of the american mathematical society, to appear. Let me conclude by outlining some of the directions and goals in this area. Since july 2018, he is the class of 1956 career development assistant professor of mathematics. If you would like to contribute, please donate online using credit card or bank transfer or mail your taxdeductible contribution to. This survey looks at some recent applications of relative entropy in additive combinatorics. Zhao yufei born january 18, 1989 is a paralympian athlete from china competing mainly in category t53 sprint events. Its definitely worth it to specifically learn some elementary number theory, various inequalities, and lots of euclidean geometry, as these are things you likely wont get in.
View the profiles of people named yufei yufei zhao. Recall from representation theory that the number of irreducible representations of a. There are versions of the regularity lemma for sparse graphs, but these only apply when the graph satisfies. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Department of psychology 1227 university of oregon eugene, or 97403 phone. Greitzer geometry unbound by kiran kedlaya combinatorics by pranav a. Graph theory and additive combinatorics yufei zhao. Yufei competed in the 2012 summer paralympics in london where he won a silver in the 100m and bronze in the 200m. On replica symmetry of large deviations in random graphs. Josef tkadlec, ilan vardi, gerhard woeginger, and yufei zhao. News mathematical institute mathematical institute. Yufei zhao won the mit school of sciences future of science award over the summer. Such functions, known as graphons, are central to the theory of graph limits, an exciting and active research area giving an analytic perspective towards graph theory.
In addition to uerenles list, some good books for this kind of stuff are the art and craft of problem solving by paul zeitz, and problem solving strategies by engel. Specifically, we examine to what extent entropyincrement arguments can replace or even outperform. It is known that each problem was correctly solved by at least 120 participants. The question came up in some work that david conlon and yufei zhao then both at oxford were doing on eigenvalues of. In the ten years since the publication of the bestselling first edition, more than 1,000 graph theory papers have been published each year. Specifically, we examine to what extent entropyincrement arguments can replace or even outperform more traditional energyincrement strategies or alternative approximation arguments based on the hahnbanach theorem. His focus is on combinatorics, discrete mathematics, and. In the exponential random graph model, one samples an nvertex random graph g with probability proportional to expfg, where fg is some. Yufei returned to mit for his phd in 2011 to study extremal, probabilistic and additive combinatorics which involved understanding how to use graph theory to better comprehend prime numbers and the links between graph and number theory. There are numerous instances when tutte has found a beautiful result in a hitherto unexplored branch of graph theory, and in several cases this has been a breakthrough, leading to the. Equiangular lines with a fixed angle and other breakthroughs from.
Buy the spectral properties of graphs on free shipping on qualified orders the spectral properties of graphs. Reflecting these advances, handbook of graph theory, second edition. Jul 09, 2018 yufei zhao, mit assistant professor of mathematics, has won the future of science award from the mit school of science for contributions to research in discrete mathematics, teaching, service, and outreach. Larry guth conjectured in his book the polynomial methods in. Mathematics genealogy project department of mathematics north dakota state university p. A bounded degree graph must have sublinear second eigenvalue multiplicity. Prove that there must be two participants such that every problem was solved by at.
I was reading maths books and solving problems, he says. The mathematics genealogy project is in need of funds to help pay for student help and other associated costs. Graph theory and additive combinatorics book project by prof. The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of. This document contains the course notes for graph theory and. We develop a sparse graph regularity method that applies to graphs with few 4cycles, including. Yufei zhao with david galvin, the number of independent sets in a graph with small. Yufei zhao class of 1956 career development assistant.
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