About me

I am Jiatu Li (李嘉图), a third-year graduate student at MIT theory group, advised by Prof. Ryan Williams.

I obtained my Bachelor’s degree from the “Yao Class”, Institute for Interdisciplinary Information Science (IIIS), Tsinghua University.

Research Interests

My research interests are about circuit complexity, meta-complexity, and proof complexity. Recently, I am interested in the following concrete directions:

• The strength of Bounded Arithmetic, the fragments of Peano that capture the complexity of reasoning (see, e.g., Youtube Talk by Sam Buss). Can we prove strong lower bounds in Cook’s theory PV\(_1\) or Buss’s theory \(S^1_2\)? Can we separate Jerabek’s theory APC\(_1\) and Cook’s PV\(_1\)? Can we identify the relative strengths of combinatorial principles and theorems as a feasible analogy of the program of Reverse Mathematics? Our partial results: APC vs PV, reverse mathematics, unprovability, unprovability’
• The complexity of the Range Avoidance Problem (see Kor21, RSW22). What is the computational complexity of finding a non-output of an \(n\)-input \((n+1)\)-output circuit? What if the circuit is a restricted one, say, an AC\(_0\) circuit? Our partial results: upper bound, lower bound 1, lower bound 2
• Proving unconditional complexity lower bounds (e.g. MW18, Chen23, CHR23, Li23) and derandomization results (e.g. CLORS23). Our partial results: catalytic, general, PRFs

As complexity theorists, our mission is to liberate the warriors trying to solve inherently hard problems. Sometimes we can use their stories to alleviate insomnia for cryptographers (see, e.g., Cryptographers Seldom Sleep Well).

I am also interested in writing formal (i.e. computer verified) mathematical proofs in Coq and Lean. Although it seems to be incredible nowadays, I believe that proof assistants will eventually be able to help mathematicians in their research (if mathematicians are not completely replaced by something like GPT-256, see, e.g., ChatGPT).¹

Selected Publications²

• Reverse Mathematics of Complexity Lower Bounds. FOCS 2024. Lijie Chen, Jiatu Li, Igor C. Oliveira. Invited to SICOMP special issue; see the Quanta article.
• The Exact Complexity of Pseudorandom Functions and the Black-Box Natural Proof Barrier for Bootstrapping Results in Computational Complexity. STOC 2022 (Best Student Paper). Zhiyuan Fan, Jiatu Li, Tianqi Yang.

Experience

• PhD Student: MIT (2023-)
  • Research Intern: NTT Research (2025 Summer), Advised by Abhishek Jain
• Undergraduate Student: Tsinghua University (2019-2023)
  • Undergraduate Research Intern: University of Warwick (2022.3-2022.7), Advised by Igor Carboni Oliveira
  • Undergraduate Research Intern: Shanghai Qi Zhi Institute (2022.8-2022.9), Advised by Yilei Chen

Interesting facts about me

• My name, Li Jiatu, is the same as the Chinese translation of Ricardo. My parents chose the name when they were reading The Capital of Karl Marx, in which the name David Ricardo occurs constantly.
• I learned Go (the chess game, not the programming language) when I was a kid and achieved amateur four-dan. Recently, I’m interested in playing go again. My ID on Fox Weiqi is jiatu1li (6d). I am a member of the MIT Go Club and you could probably catch me in the meetings (check https://www.meetup.com/massgo/ for the schedule).