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 and geometric group theory. 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. I trained with Club de karate de Sainte-Foy in Quebec city (QC, AKJQ-IKD), Centre de karate shotokan Laval in Laval (QC, AKJQ-IKD), HQ Honbu Upper Beaches in Toronto (ON, IKD) and ÉTS dojo in Montreal (QC, JKA). In kendo, I started with the Ayame dojo in Montreal, and am currently with the Pitt kendo dojo in Pittsburgh. 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:
Coeur Yoyo by Laura Doyle Pean, reminding us of our very first heartbreak;
Ru by Kim Thuy, 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.

My pet bunny (named Jiao) has an instagram page.

Research and 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].

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

Lower bound methods for sign-rank and their limitations
with Hamed Hatami, Pooya Hatami, William Pires, Rosie Zhao.

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].