Yufei Zhao
@yufeizhao
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Associate Professor of Mathematics, MIT
Cambridge, MA
Joined July 2011
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My most loyal reader 📖
(Pre)order your copy:
Publisher:
(There is a link to recommend my book to your library)
Amazon:
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I'm writing a textbook titled Graph Theory and Additive Combinatorics, based on an intro grad-level class that I'm teaching right now for the third time.
The book draft is still very much a work in progress. More chapters will be added. Feedback welcome!
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Putnam Math Competition results released! Congratulations to everyone!
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Congratulations to Jinyoung Park and Huy Pham for proving the Kahn-Kalai conjecture---a central open problem in probabilistic combinatorics. Truly exciting breakthrough!
The story of Jinyoung's extraordinary path to mathematics:
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My book coming out soon!
Graph Theory and Additive Combinatorics by
@yufeizhao
An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
📚
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An updated version of my lecture notes on the probabilistic method in combinatorics:
(just finished teaching the last class this semester 😀)
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MIT students dominate the Putnam Math Competition once again! 🍾
Full results:
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These days I feel a strong urge to go back to reading "old" and classic math papers and foundational books, to re-learn the "basics" revisit what got me interested in what I'm doing in the first place, instead of constantly trying to keep up with what's new.
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I like math papers that either
(1) show how "easy" some problem is (e.g., 2 page proof)
(2) show how "hard" some problem is (e.g., deep connections)
I love papers that do both
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Carl Schildkraut, an MIT undergrad, disproved a conjecture about equiangular lines that I had previously believed in. His new paper offers clever new constructions of graphs with high second eigenvalue multiplicity. I blogged about it here
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We proved the Bollobás–Brightwell–Leader conjecture that nearly all k-SAT functions are unate.
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I plan to polish these lecture notes into a book, and now seems like a good time to start
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I’m delighted to showcase and celebrate a selection of recent papers by the talented combinatorialists at MIT, especially those by students and postdocs. These papers reflect the culmination of their hard work, dedication, and innovative problem solving.
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Amazing new work by Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, and Michael Simkin.
They proved a 1973 Erdős conjecture that high girth Steiner triple systems exist.
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MIT students took 70% of the honorable mentions and above this year, up from about 60% last year, and about 50% the previous time.
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MIT News reporting on my team's research on equiangular lines
Mathematicians solve an old geometry problem on equiangular lines: How many lines can be pairwise separated by the same angle in high dimensions? Geometry breakthrough gives new insights into spectral graph theory.
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Exciting new breakthrough from Ashwin Sah: a new upper bound for Ramsey numbers
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A profile of the Putnam Seminar that I've been teaching at MIT since 2017
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Congratulations to new Clay Research Fellows Ishan Levy and Mehtaab Sawhney!
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Don’t initialize first names when citing references
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@MITOCW
site for my course Graph Theory and Additive Combinatorics is now live, complete with lecture videos and course notes:
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Blog post on amazing new results by Vishesh Jain, Ashwin Sah, and Mehtaab Sawhney on the singularity problem for random matrices:
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My student Ashwin Sah was featured in Quanta Magazine
Senior mathematicians told me they've never seen anything like the research output Ashwin Sah and Mehtaab Sawhney produced together as undergrads at MIT. My new story for
@QuantaMagazine
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Congratulations to Ashwin Sah and Mehtaab Sawhney for winning the 2021 Morgan Prize! Well deserved!
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Jokes aside, writing a good math paper should be like telling an engaging story.
Who are the characters? What are their drives? Who are the villains? Where are the obstacles? Conflict? Suspense? Climax? Ending?
On arXiv today, one of the strangest math papers I've seen: a proof of a result in metric geometry in the form of a fantasy novellette.
According to the acknowledgments, the paper is a retort by the author against those who complain that his research articles are too verbose.
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How many k-SAT functions are there?
What does a typical k-SAT function look like?
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Working from home as a mathematician:
1. Upload papers I want to read to my Remarkable tablet
2. Brew a cup of 🍵
3. Find a place to sit without any internet browsing device within arms' reach
4. Read
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@wtgowers
MIT and Harvard got once sued for lacking closed captioning on lecture videos. So there's deterrent
I recently went through the process of publishing my videos on MITOCW. I learned that youtube auto-captioning doesn't qualify
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Too often a math paper reads like:
Guy walks 1km forward.
Turns left and walks 100m.
Turns right and walks 1km.
Enters castle and slays the dragon.
... without every telling us that there was a huge rock blocking his way!
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Lecture videos also hosted on Youtube
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Our new paper constructing graphs with high second eigenvalue multiplicity.
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The high dimensional sphere comes many surprising and counterintuitive features. Here is one of them.
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@wtgowers
I read this wonderful survey by Keith Ball in grad school, which opened my eyes to so many counterintuitive phenomena in high dimensions
So top of my list would be the classic papers of Milman to see how asymptotic geometric analysis began as a subject
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Congratulations to
@theyisun
and
@jonathanpwang
for their new exciting venture
@axiom_xyz
using zero-knowledge proofs to enhance computation on the decentralized web
We are announcing Axiom, the ZK coprocessor for Ethereum:
Axiom provides smart contracts trustless access to all on-chain data and arbitrary expressive compute over it. Like GPUs do for CPUs, Axiom augments blockchain consensus with zero-knowledge proofs.
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I wrote a blog post on my final-year PhD student Ben Gunby's work showing some surprising new phenomenon for the upper tail problem for random regular graphs
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The intersection of a high-dimensional convex body with a random rotation of itself looks like a ball ⚽︎
I learned this last night while reading the wonderful preface of
Also, high dimensional convex bodies look like starfish ⭐️
@optiML
@yufeizhao
I meant that in 2019 one sort of randomly hoped that an intersection would take place. In 2020 it has dawned on us that we can intersect whenever we want.
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- Top five winners (Fellows) all come from MIT, including:
- 3rd time Fellow for Shengtong Zhang
- 2nd time Fellow for Daniel Zhu
- also: Andrew Gu, Michael Ren, and Edward Wan
- Dain Kim is the Elizabeth Lowell Putnam prize winner
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This year, 187 MIT students took the intense six-hour Putnam Competition exam. That's a 25% increase from last year.
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A big transition that I experienced in going from a grad student/postdoc to a faculty member is that now I often find myself juggling many different projects and responsibilities.
I enjoyed this 8-part Oatmeal comic on creativity, and this one really struck a chord
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Giving a talk to a live audience: make eye contact, get visual feedback on audience engagement
Giving a talk on
@zoom_us
: avoid looking at distracting chat box messages or audience videos (they're probably looking at something else anyway)
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I lagged behind in blogging about many interesting and exciting projects that my students and I have been working on lately. So I plan to write a few "catch up" blog posts on what we have been up to.
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> “This class builds connections,” says Zhao. “All of them are new to MIT, and many are arriving in the U.S. for their first time. They are all interested in mathematics. I hope that the seminar will help them meet other students and form a supportive community.”
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> The seminar is internationally diverse, with students from 10 countries outside the United States: Australia, Armenia, Canada, China, Georgia, India, Korea, Portugal, Singapore, and Thailand.
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New paper solving a classic problem in incidence geometry: how many joints can L lines make?
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@cheraghchi
@thegautamkamath
I addressed this issue in my blog post. The simplest and most consistent method is to use the author names as they appear in the original publication
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First up, my paper with PhD student Jonathan Tidor and undergraduate student Hung-Hsun Hans Yu solving the joints problem for varieties
(P.S. I've migrated my blog from Wordpress to now integrated as part of my personal homepage)
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@wtgowers
I don't know any such cases. In principle, there could be issues since the lectures are affiliated with the university.
@karpathy
had to unfortunately take down his lectures due to legal concerns
I regret to inform that we were forced to take down CS231n videos due to legal concerns. Only 1/4 million views of society benefit served :(
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@topherchang
@_Dave__White_
Math competitions are a fun and exciting way to get kids excited about mathematics. Will this development aid or hinder this outreach effort? 🤷
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@ccanonne_
I agree with you that this Wikipedia entry is very misleadingand and arguably wrong. You’ll do the community a service by correcting it!
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