Feeling depressed and anxious about the state of the world? Try working on a 375 year-old math problem from the Platonic realm, which should be completely psychologically safe . . . youtu.be/QH4MviUE0_s

Please take a minute and nominate your favourite paper from FOCS 1995, 2005, or 2015 for the FOCS Test Of Time Award! 1995 papers: dblp.org/db/conf/focs... 2005 papers: dblp.org/db/conf/focs... 2015 papers: dblp.org/db/conf/focs... Nomination instructions here: tc.computer.org/tcmf/2025/08...

NSF announces funding for ICARM: the Institute for Computer-Aided Reasoning in Mathematics, based in Carnegie-Mellon . Amazing! Carnegie-Mellon press release here: www.cmu.edu/news/stories... www.nsf.gov/news/nsf-inv...

After 3 1/2 years of work my course on quantum computing is finally finished — the "Director's Cut" of Understanding Quantum Information and Computation is now available. arxiv.org/abs/2507.11536

New work with @booleananalysis.bsky.social! We prove instance-optimal bounds for quantum state certification when testers can measure all copies simultaneously, finding that the optimal copy complexity depends on how close to maximally mixed the hypothesis state is. arxiv.org/abs/2507.06010 1/3

Spread the word: there is a new prize in Theoretical Computer Science in honor of Luca Trevisan-- cs.unibocconi.eu/call-nominat... (Intent-to-nominate letters due by July 31.)

Sigbovik's looking good this year. Come for the tom7/suckerpinch video preview, stay for Shor vs a random number generator...

#STOC2025 (June 23-27, Prague) Theory Fest is looking for workshop proposals. The deadline is March 9th. Apply here: stoc2025theoryfest.netlify.app

New paper: Simulating Time With Square-Root Space people.csail.mit.edu/rrw/time-vs-... It's still hard for me to believe it myself, but I seem to have shown that TIME[t] is contained in SPACE[sqrt{t log t}]. To appear in STOC. Comments are very welcome!

PL puzzle. Say we have instructions called "x1 += x2", "x2 += x3", "x3 += x4", and versions with "-=" that cancel them. We define a program "x1 += x2" "x2 += x3" "x1 -= x2" "x2 -= x3", and abbreviate it "x1 -= x3". We similarly define "x2 -= x4". We posit that "x1 -= x3" commutes with [...]

Group theory puzzle. We have symbols ♀️,🏁,♂️. Also define ♕=♀️🏁♀️⁻¹🏁⁻¹ and ♔=♂️🏁♂️⁻¹🏁⁻¹. We posit: ♀️♕=♕♀️ and 🏁♕=♕🏁 and ♂️♔=♔♂️ and 🏁♔=♔🏁. And we posit: ♀️²⁰²⁵=🏁²⁰²⁵=♂️²⁰²⁵=1 (identity). Can you prove ♕♔=♔♕?

Cayden Codel & Noah Singer have formalized in Lean the climactic theorems of the Kaufman-Oppenheim paper that shows the A_3-type coset complex HDXs are cosystolic expanders! (I.e., Sec. 7.2 of arxiv.org/abs/1907.01259) It's a warmup for the main project...

Bravo to 1st-year undergraduate Tyler Yang at CMU, who was the first person to write up and make videos for all* 100 exercises in my "Quantum Computer Programming in 100 Easy Lessons" series! (www.youtube.com/watch?v=XtDJ...) *more or less all

Random d-regular graphs are (2-sided) Ramanujan with probability 69%: arxiv.org/pdf/2412.20263 by Jiaoyang Huang, Theo Mckenzie, HT Yau. In particular, infinitely many 7-regular Ramanujan graphs exist.

In case you're in Cambridge, MA on Tue. Dec. 10, I'll give a talk at 4pm (MIT 32-G449) about coboundary expansion in high-dimensional expanders. It's kind of about group theory, though. toc.csail.mit.edu/node/1671 Besides coauthor Noah Singer (@singerng_), here's the cast of characters:

Bhangale, Khot, Liu, and Minzer improved the bounds for combinatorial lines of length 3, established in the Polymath project on the Hales-Jewett problem. Interestingly, this is done from a TCS perspective using pseudorandomness and inverse theorems for CSPs. eccc.weizmann.ac.il/report/2024/...

Great new quantum algorithm for approximate polynomial interpolation on the arXiv today: "given a uniformly random vector y of F_q^q, some integers k<q and u < q/2, find a polynomial P(x) of degree <k such that |P(i)-y_i| < u for all i". quantum computers can help here (1/4)