His focus is on combinatorics, discrete mathematics, and. Dec 16, 2019 conference on graph theory and its applications. 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. David conlons research works university of oxford, oxford. On replica symmetry of large deviations in random graphs. Transactions of the american mathematical society, to appear. Yufei zhao class of 1956 career development assistant. Graph theory and additive combinatorics, taught by prof.
The mathematics genealogy project is in need of funds to help pay for student help and other associated costs. This survey looks at some recent applications of relative entropy in additive combinatorics. The question came up in some work that david conlon and yufei zhao then both at oxford were doing on eigenvalues of. S997, graph theory and additive combinatorics, fall 2017, yufei zhao. Greitzer geometry unbound by kiran kedlaya combinatorics by pranav a. Yufei zhao graduated in 2010, received his phd in 2015, and is now the class of 1956 career development assistant professor at mit. Yufei competed in the 2012 summer paralympics in london where he won a silver. Everyday low prices and free delivery on eligible orders. 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. Yufei zhao joined the mathematics faculty as assistant professor in july 2017. Limits, sparse random graph models, and power law distributions authors. 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. He received his sb in mathematics and computer science from mit in 2010, his masters of advanced study in mathematics. This is the homepage for a textbook that i plan to write.
Acknowledgement much of the material in these notes is from the books graph theory by reinhard diestel, introductiontographtheory. The celebrated greentao theorem states that there are arbitrarily long arithmetic progressions in the primes. Aug 14, 2018 buy sparse optimization theory and methods 1 by zhao, yunbin isbn. There are numerous instances when tutte has found a beautiful result in a. 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. Equiangular lines with a fixed angle with zilin jiang, jonathan tidor, yuan yao, and shengtong zhang advances in mathematics 319 2017, 3347.
Imc 2002 two hundred students participated in a mathematical contest. I didnt set out to study highdimensional footballs for their own sake. Let me conclude by outlining some of the directions and goals in this area. Yufei zhao teaching graph theory and additive combinatorics.
His focus is on combinatorics, discrete mathematics, and graph theory. Journal of combinatorial theory, series b vol 8, pages 1. We develop a sparse graph regularity method that applies to graphs with few 4cycles, including. 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. If you would like to contribute, please donate online using credit card or bank transfer or mail your taxdeductible contribution to. In 2, the authors systematically study the local structure of differentiable graphon parameters. Mathematics genealogy project department of mathematics north dakota state university p. Yufei zhao with david galvin, the number of independent sets in a graph with small. 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. His current research interests include the genus distribution of graphs, computer graphics, and knot theory. It is known that each problem was correctly solved by at least 120 participants. Independence problem solved through collaboration mit news. Much of the material in these notes is from the books graph theory by reinhard diestel, intro ductiontographtheory bydouglaswest,andproofsfromthebook bymartinaignerandgunter ziegler.
Prove that there must be two participants such that every problem was solved by at. This is the second iteration of a course i first taught two years ago. 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. The earliest result in extremal graph theory is usually credited to mantel, who proved, in 1907.
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. Zhao, the number of independent sets in a regular graph, combin probab comput volume 19 2010, pp. A bounded degree graph must have sublinear second eigenvalue multiplicity. Yufei zhao simons institute for the theory of computing. Tufte this book is formatted using the tuftebook class. Yufei zhao, sets characterized by missing sums and differences, journal of number theory, 11 2011 210724. In the ten years since the publication of the bestselling first edition, more than 1,000 graph theory papers have been published each year. I was reading maths books and solving problems, he says. Equiangular lines with a fixed angle and other breakthroughs from. Department of mathematics yufei zhao joined the mathematics faculty as assistant professor in july 2017. There are versions of the regularity lemma for sparse graphs, but these only apply when the graph satisfies.
Join facebook to connect with yufei yufei zhao and others you may know. Specifically, we examine to what extent entropyincrement arguments can replace or even outperform. Zhao yufei born january 18, 1989 is a paralympian athlete from china competing mainly in category t53 sprint events. We prove our main result via a new insight in spectral graph theory, namely.
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. Josef tkadlec, ilan vardi, gerhard woeginger, and yufei zhao. Handbook of graph theory discrete mathematics and its. 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. News mathematical institute mathematical institute. 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. Buy sparse optimization theory and methods 1 by zhao, yunbin isbn. Understanding the limitations of the regularity lemmain the regularity partition, how does the number of parts depend on the regularity parameter.
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. Yufei zhao won the mit school of sciences future of science award over the summer. William lowell putnam mathematical competition wikipedia. 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. Buy the spectral properties of graphs on free shipping on qualified orders the spectral properties of graphs. A recipient of numerous awards and research grants, dr. In the exponential random graph model, one samples an nvertex random graph g with probability proportional to expfg, where fg is some. Limits, sparse random graph models, and power law distributions.
Graph theory and additive combinatorics book project by prof. Graph theory and additive combinatorics mathematics 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. David conlons research while affiliated with university of oxford and other places. 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. See the complete profile on linkedin and discover yufeis. Sep 07, 2012 graph regularity is an active research area.
Reflecting these advances, handbook of graph theory, second edition. This document contains the course notes for graph theory and. The post is based on a talk i gave earlier today at a graduate student. Yufei zhao large deviations and exponential random graphs. Bibliography of the duluth summer research programs. Yufei competed in the 2012 summer paralympics in london where he won a silver in the 100m and bronze in the 200m. Larry guth conjectured in his book the polynomial methods in. Ams transactions of the american mathematical society.
Since july 2018, he is the class of 1956 career development assistant professor of mathematics. Yufei zhao massachusetts institute of technology verified email at mit. 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. Online books by topic number theory by justin stevens number theory by david santos geometry revisited by h. Imo training 2010 projective geometry alexander remorov poles and polars given a circle. 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. 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. Recall from representation theory that the number of irreducible representations of a. View the profiles of people named yufei yufei zhao. View yufei zhaos profile on linkedin, the worlds largest professional community.
Department of psychology 1227 university of oregon eugene, or 97403 phone. If you would like to contribute, please donate online using credit card or bank transfer or mail. Zhao da yuan is the author of practical qin na part two 5. On derivatives of graphon parameters sciencedirect. I wanted to create a set of notes, eventually turning into a new textbook, that. Results may not be complete and may include mistakes. 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. Extremal and ramsey results on graph blowups, 2019. Greitzer geometry unbound by kiran kedlaya combinatorics by. David conlons 103 research works with 1,328 citations and 5,738 reads, including.
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