Computational Complexity

For our next favorite theorem, we look at the surprising power of provers who share entangled bits. If you can prove something to an arbitrarily computable verifier, then two entangled provers ca...

https://blog.computationalcomplexity.org/2024/04/favorite-theorems-quantum-provers.html

 Recently 1) Avi Wigderson won the Turing Award (See blog posts by Fortnow-here , Scott-here , Lipton-Regan here , and the ACM announcement here ).  The last time I could find when Fortnow-G...

https://blog.computationalcomplexity.org/2024/04/avi-wigderson-is-counterexample-to-two.html

The ACM announced that Avi Wigderson, a force in computational complexity and beyond, will receive the 2023 A. M. Turing Award (Quanta article ). This is the first primarily complexity theorist...

https://blog.computationalcomplexity.org/2024/04/avi-wins-turing-award.html

  My friend and colleague Rance Cleaveland passed away on March 27, 2024 at the age of 62.  He was a professor at The University of Maryland at College Park in the Computer Science Department. ...

https://blog.computationalcomplexity.org/2024/04/rance-cleaveland-passed-away-on-march.html

 In a prior post I asked the following question: find x,y,z positive natural numbers such that the following is true: $$ frac{x}{y+z} + frac{y}{x+z} + frac{z}{x+y} = 4. $$ I first saw the ...

https://blog.computationalcomplexity.org/2024/04/answer-to-question-metaquestion-remains.html

 1) Question: find x,y,z natural numbers such that the following is true: $$ frac{x}{y+z} + frac{y}{x+z} + frac{z}{x+y} = 4. $$ I was first presented the problem a more fun way: (NOTE- ...

https://blog.computationalcomplexity.org/2024/04/a-math-question-and-meta-question.html

Tech companies are performing exceptionally well, driving the S&P 500 to new heights with their soaring stock prices. However, the tech sector, apart from AI, expects a job decline to persist t...

https://blog.computationalcomplexity.org/2024/03/the-softening-of-computing-jobs-blip-or.html

 I am looking at LOTS of transcript of students who applied for my program REU-CAAR  so I sometimes come across grades that I don't understand. The transcript does not have a guide to them, an...

https://blog.computationalcomplexity.org/2024/03/i-know-what-b-c-d-f-mean-but-what-about.html

In the recent academy award winning movie Oppenheimer , Niels Bohr tests a young Oppenheimer. > BOHR: Algebra's like sheet music, the important thing isn't can you > read music, i...

https://blog.computationalcomplexity.org/2024/03/can-you-feel-machine.html

(Harry Lewis helped me with this post.) March 15 was UMCP Computer Science Grad Student Visit Day. I suspect many of my readers are at schools that had their Grad Student Visit Day recently, or...

https://blog.computationalcomplexity.org/2024/03/grad-student-visit-day-that-was-then.html

La Scala in Milan Google translate generally impresses but consider this translation from a short Italian news article . I boldfaced a few items. > Not scheduled at the premiere of M...

https://blog.computationalcomplexity.org/2024/03/translation-in-context.html

 In the 1980's and 1990's when I got a paper accepted to a journal or conference  it seemed important to see it in print. Having a paper accepted was nice, but it didn't seem real until I held ...

https://blog.computationalcomplexity.org/2024/03/the-thrill-of-seeing-your-name-in-print.html

Our next favorite theorem gave a relatively simple proof of the sensitivity conjecture, a long-standing problem of Boolean functions. Induced subgraphs of hypercubes and a proof of the Sensitiv...

https://blog.computationalcomplexity.org/2024/03/favorite-theorems-sensitivity.html

There is an article about the letter Richard Duffin wrote for John Nash that helped John Nash get into Princeton: here . The title of the article is  The Best Recommendation Letter Ever. Th...

https://blog.computationalcomplexity.org/2024/03/the-letter-to-recommend-john-nash-was.html

Illinois' most famous citizen working on a quantum computer The governor of Illinois, JB Pritzker, unveiled his budget last week including $500 million for quantum computing research . Is thi...

https://blog.computationalcomplexity.org/2024/02/a-quantum-state.html

(This post was inspired by Lance's tweet and later post on part of IP=PSPACE being formally verified.)  We now have the means to verify that a proof (prob just some proofs)  is correct (one...

https://blog.computationalcomplexity.org/2024/02/when-is-it-worth-time-and-effort-to.html

Last summer as I lamented that my research didn't have real world implications, one of the comments mentioned the sumcheck protocol used for zero-knowledge SNARKs. I tried to figure out the conn...

https://blog.computationalcomplexity.org/2024/02/sumchecks-and-snarks.html

Lance did a post on Babai's result on Graph Isomorphism (see here ). I then did a post asking if Graph Isomorphism has real applications (see here ).  Lance proofread my post (There were some ty...

https://blog.computationalcomplexity.org/2024/02/chatgpt-thinks-graph-isomorphism-has.html

An academic field often organizes itself pulling ideas from its own field. For example, students on the economics faculty job search can signal at most two schools , without giving any other rul...

https://blog.computationalcomplexity.org/2024/02/focusing-on-te.html

Lance's post on Babai's result on Graph Isomorphism (henceforth GI) inspired some random thoughts on GI. (Lance's post is here .)  1) Here is a conversation with someone who I will call DAVE. ...

https://blog.computationalcomplexity.org/2024/02/are-there-any-real-applications-of.html

We start our favorite theorems of the last decade with a blockbuster improvement in a long-standing problem.  Graph Isomorphism in Quasipolynomial Time by László Babai The graph isomorph...

https://blog.computationalcomplexity.org/2024/02/favorite-theorems-graph-isomorphism.html

 I got an email from an organization that wants to publicize one of my papers. Which paper did they want to publicize? 1) If the organization was Quanta, they are KNOWN so I would trust it. In...

https://blog.computationalcomplexity.org/2024/02/the-advantage-of-working-on-obscue.html

Seems like US universities have been in the news quite a bit recently. You'd think for the great academics and research. Alas, no. I decided to make a list of the not so unrelated topics. The l...

https://blog.computationalcomplexity.org/2024/01/university-challenges.html

 (This post was done with the help of Max Burkes and Larry Washington.) During this post (N= {0,1,2,ldots }) and  (N^+={1,2,3,ldots }). RECALL: Hilbert's 10th problem was to (in todays terms...

https://blog.computationalcomplexity.org/2024/01/certifying-number-is-in-set-using.html

The following request came from a comment  earlier this month (shortened) > Could you give some advice on how to study complexity theory on > one's own, and/or to follow the ...

https://blog.computationalcomplexity.org/2024/01/learning-complexity-on-your-own.html