Let me conclude by outlining some of the directions and goals in this area. 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. Kavish gandhi massachusetts institute of technology. Yufei zhao works in extremal, probabilistic, and additive combinatorics. His focus is on combinatorics, discrete mathematics, and graph theory. The concept was introduced to represent unsharp concepts such as humans being tall or young or a. This gives the rst broadly applicable limit theory for sparse graphs with unbounded average degrees. We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. My major interest lies in program optimization, especially from the. We build on the work of galvin and tetali, who studied the number of graph. Yufei zhao large deviations and exponential random graphs. He and ruzsa used the graph regularity lemma to give a new, graph theoretic proof of roths theorem.
Zhao yufei born january 18, 1989 is a paralympian athlete from china competing mainly in category t53 sprint events. Just a word about how about this problem is related to a bigger picture. Prior to returning to mit, yufei was the esmee fairbairn junior research fellow in mathematics at new college, oxford, as well as a research fellow at the simons institute for the theory of computing at uc berkeley. A directed graph is impartial if and only if every component is recursively bridgemirrored trees. June 27 to july 9, 2008 summer camp participants, including local students imo team. Under suitable restrictions on node weights, we prove the. Wilfrid laurier university in waterloo, ontario dates.
An independent set in a graph is a subset of vertices such that no two of them are joined by an edge. Recall from representation theory that the number of irreducible representations of a. Yufei zhao mit solving a longstanding problem in discrete geometry, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. Jun 21, 2016 sparsitydriven image recovery methods assume that images of interest can be sparsely approximated under some suitable system. The number of independent sets in a regular graph combinatorics, probability and computing 19 2010, 315320. A key ingredient is a new result in spectral graph theory.
He received his mit phd under jacob fox in 2015, and was a postdoctoral fellow at the university of oxford. The number of independent sets in a regular graph volume 19 issue 2 yufei zhao skip to main content accessibility help we use cookies to distinguish you from other users and to. For us, it will serve as a tool to deduce the cauchybinet formula. 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. Much of the material in these notes is from the books graph theory by. Jonathan tidors research works massachusetts institute of. The number of independent sets in a graph with small. Independence problem solved through collaboration mit news. We extend the lp theory of sparse graph limits, which was introduced in a companion paper, by analyzing diff\u000berent notions of convergence. The post is based on a talk i gave earlier today at a graduate student lunch seminar. This result generalizes a recently resolved conjecture of alon and kahn on the number of independent sets.
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. This settles a conjecture of alon in 1991 and kahn in 2001. 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. We begin, in section 2, by presenting the ruzsaszemer edi graph theoretic approach to roths theorem. Yufei zhao is a junior research fellow in mathematics at new college, oxford.
Results may not be complete and may include mistakes. The mathematics genealogy project is in need of funds to help pay for student help and other associated costs. Ld convergence, quotients, and right convergence c borgs, jt chayes, h cohn, y zhao the annals of probability 46 1, 337396, 2018. Browse other questions tagged binatorics graph theory inequalities extremal graph theory. Imo training 2010 projective geometry alexander remorov poles and polars given a circle. You structured problem sets a little differently in this course, providing students. Abstractlet indg be the number of independent sets in a graph g. Limits, sparse random graph models, and power law distributions.
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. Mathematics genealogy project department of mathematics north dakota state university p. Below, professor yufei zhao describes various aspects of how he taught 18. Yufei huang professor department of electrical and computer engineering, university of texas at san antonio adjunct professor department of epidemiology and biostatistics, university of texas health science center at san antonio cv biosketch yufei huang received his ph. Sep 07, 2012 graph regularity is an active research area. More generally, we prove a graphical brascamplieb type inequality, where every edge of g is assigned. We prove our main result via a new insight in spectral graph theory. Expander graphs and their applications request pdf. There have been enduring efforts on constructing discrete frames and tight. This paper examines the theory of kernel fisher discriminant analysis kfd in a hilbert space and develops a twophase kfd framework, i. My major interest lies in program optimization, especially from the perspective of input sensitivity, parallelization, and redundant computation elimination.
A framework for flexible migration of program profiles across software versions mingzhou zhou, bo wu, yufei. View yufei zhao s profile on linkedin, the worlds largest professional community. Before giving a very short cauchyschwarz inequality proof for the 3edge path can be done in a similar fashion for any tree, let me comment on the authorship of the inequality in question. I am working through the work of baoding liu on uncertainty theory, specifically uncertain sets.
Under suitable restrictions on node weights, we prove the equivalence of metric convergence, quotient convergence, microcanonical ground state energy convergence, microcanonical free energy convergence, and large deviation convergence. Yufei zhao class of 1956 career development assistant. Generalizations of the theory and deployment of triangular inequality for compilerbased strength reduction yufei ding, lin ning, hui guan, xipeng shen. Szemeredis regularity lemmaa powerful tool in combinatorics that provides an approximate descriptiondecomposition for every large graph. Yufei zhao joined the mathematics faculty as assistant professor in july 2017. Ramsey theory, graph theory, combinatorial geometry, and applications of combinatorics to computer science. We extend the lp theory of sparse graph limits, which was introduced in a companion paper, by analyzing diff erent notions of convergence. Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated. Zhijia zhao zh sounds like j assistant professor riple research group computer science and engineering, uc riverside. A powerful tool in combinatorics that provides an approximate description decomposition for every large graph. He has been developing tools that connect graph theory with additive. This conference will invite experts on graph theory to exchange idea at the. The bipartite swapping trick on graph homomorphisms.
If you would like to contribute, please donate online using credit card or bank transfer or mail your taxdeductible contribution to. Szemeredis regularity lemma 26 is one of the most powerful tools in graph theory. Class of 1956 career development assistant professor. The math olympiad program in india aims to encourage the students interested in.
Contribute to programthinkzhao development by creating an account on github. Emory university, georgia tech and georgia state university, with support from the national science foundation and national security agency, will continue the series of miniconferences from 20192020. The number of independent sets in a graph with small maximum degree with david galvin graphs and combinatorics 27 2011, 177186. For six hours she and 4,622 other undergraduates from 568 institutions in the united states and canada struggled over enigmatic problems involving group theory, set theory, graph theory, lattice theory, and number theory. See the complete profile on linkedin and discover yufeis. View the profiles of professionals named yufei zhao on linkedin. As discontinuities of 2d images often show geometrical regularities along image edges with different orientations, an effective sparsifying system should have high orientation selectivity. In this paper, we lay the foundations of the lp theory of graphons, characterize convergence, and develop corresponding random graph. Theory and practice, january 68, 2016, uc san diego. Yufei ding, yue zhao, xipeng shen, madan musuvathi, todd mytkowicz.
It can be considered as the equality case for a directed analog of an open problem known as sidorenkos conjecture. 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. Yufei zhao assistant professor of mathematics at massachusetts institute of technology large deviations and exponential random graphs thu, may 3, 2018 2. Jonathan tidors research works massachusetts institute. Kahn proved the bound when the graph is assumed to be bipartite. Theory and practice, january 68, 2016, uc san diego abstracts anima anandkumar uc irvine. S997 graph theory and additive combinatorics yufei zhao. Equiangular lines and eigenvalue multiplicities mathematics.
Yufei zhao simons institute for the theory of computing. It is related to a number of other graph homomorphism inequalities that are central in extremal graph theory. One direction of this follows from the expander mixing lemma, while the other requires the assumption that the graph is a cayley graph. In the exponential random graph model, one samples an nvertex random graph g with probability proportional to expfg, where fg is some graph. Worked with laszlo lovasz and noah golowich from january 20 to june 2014, yufei zhao from january 2014 to january 2015, and. If you would like to contribute, please donate online using credit card or bank transfer or mail. On regularity lemmas and their algorithmic applications. I am joining the department of computer science, university of california at santa barbara as an assistant professor in nov 2017. Zilin jiang, jonathan tidor, yuan yao, shengtong zhang, yufei zhao submitted on 29 jul 2019 v1, last revised 4 aug 2019 this version, v2 abstract. A34 and graph theory and additive combinatorics, 18. Johan ugander, microsoft research redmondstanford university graph cluster randomization.
See the complete profile on linkedin and discover yufei s. However, as proven by david conlon and yufei zhao in 2017, slight variants of the discrepancy and eigenvalue conditions for regular cayley graphs are equivalent up to linear scaling in. Cauchyschwarz proof of sidorenko for 3edge path blakley roy inequality ask question. Yufei competed in the 2012 summer paralympics in london where he won a silver in the 100m and bronze in the 200m.
Hypergraph expanders of all uniformities from cayley graphs with david conlon and jonathan tidor. Mit math professor yufei zhao gives his undergraduates a frustrating. 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. The bipartite swapping trick on graph homomorphisms siam. Petersburg students in a school go for ice cream in groups of at least two. Performed research in extremal combinatorics and graph theory. Trainer at us math olympiad summer program, lincoln, nebraska. A powerful tool in combinatorics that provides an approximate descriptiondecomposition for every large graph. Understanding the limitations of the regularity lemmain the regularity partition, how does the number of parts depend on the regularity parameter. The acm sigplan conference on programming language design and implementation 2017.