Ran Tao


image of me


Hey there!
I am currently a PhD student at Carnegie Mellon University. My main research interests lie within measured group theory, countable Borel equivalence relations, descriptive set theory, geometric group theory and topology. Previously I was a master's student at McGill University, advised by Anush Tserunyan.

Drop me an email: rant2 (at) andrew (dot) cmu (dot) edu


About me

I am a martial arts practitioner. I have been training in Shotokan karate since 2012, and recently sprouted an interest in kendo and aikido. I trained with
Club de karaté de Sainte-Foy in Québec city (QC, AKJQ-IKD);
Centre de karaté shotokan Laval (QC, AKJQ-IKD);
HQ Honbu Upper Beaches in Toronto (ON, IKD); and
ÉTS dojo in Montréal (QC, JKA).
Martial arts for me is the pursuit of a better self, which so happens to exhibit a physical form.

Life is full of things to enjoy, among which sits the best company to rainy afternoons. Some discoveries that I find particularly resonating include:
Tomorrow, and Tomorrow, and Tomorrow by Gabrielle Zeving, a prose close the soul, grounded in the earth;
Ru by Kim Thúy, gives us crude pieces of memories of her childhood during the darkest time of Vietnam's history;
Folle by Nelly Arcan, a chaotic, suicidal free spirit questioning axioms of the universe.

Academic works

Tree-like graphings, wallings, and median graphings of equivalence relations.
with Ruiyuan (Ronnie) Chen, Antoine Poulin and Anush Tserunyan.
Coming soon. [arXiv].

Master's thesis: Measured countable Borel equivalence relations.
advised by Anush Tserunyan, novel results are joint with Anush Tserunyan.
[link to thesis] with errata (last updated October 30, 2024) [link].

On the multiplicative independence between n and ⌊nα⌋.
with David Crnčevíc, Felipe Hernández, Kevin Rizk and Khunpob Sereesuchart.
To appear. [arXiv].

Lower bound methods for sign-rank and their limitations
with Hamed Hatami, Pooya Hatami, William Pires, Rosie Zhao.
APPROX-RANDOM 2022. [ECCC].

Separations in Proof Complexity and TFNP
with Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere.
FOCS 2022. [ECCC].

Further collapses in TFNP
with Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere.
CCC 2022. [DROPS].

On public-coin zero-error randomized communication complexity
with Ben Davis, Hamed Hatami, William Pires, Hamza Usmani.
Information Processing Letters 2021. [ECCC].