Updated Date

16th July, 2026

Who I Am

I am Yapeng Zhao, a student just graduated from Peking University in China and will become a PhD student at the University of Toronto this September.

My Academic Interests

Generally, I am interested in mathematical physics, but I do have broad interests in both mathematics and sciences.

Currently, I am particularly interested in phase transitions, especially in developing a dictionary that relates graphs, classes of models, and phase transitions, and in identifying concrete physical or chemical systems that realize each type of behavior.

A Broader Motivation

Hilbert’s sixth problem was partially solved by Andrey Kolmogorov in the 1930s by putting probability theory on an axiomatic basis. The most recent advance is the derivation of fluid equations via Boltzmann’s kinetic theory in 2025. However, infinitely many open problems remain, including deriving these equations from more reliable and realistic models, establishing a rigorous mathematical foundation for AI, and addressing the original formulation of Hilbert’s sixth problem: the axiomatization of physical theories.

At present, I am deeply absorbed in exploring the limits of AI in mathematics.

My Hobbies

I love sports and I am an outdoorsy people.

I am an amateur runner, interested in 5k, 10k, half marathons and full marathons. I have run a marathon in 3h15min, but I was injured at the end of 2025. It took me over six months to recover!

I love trail running as well, I enjoy running across rivers in the mountains, watching beautiful sightseeings at the same time! I hope that one day I can climb snow-covered mountains.

I am interested in French opera and traditional Chinese-style music.

Research Projects

I finished a project at the interface of mathematics and chemistry under the supervision of Zhiqiang Li at Peking University. The project has been submitted. See Reactive Oxygen Pool over Ceria Enables Catalytic Oscillation if you are interested. Here is the presentation about our work: Chemical Oscillation and Limit Cycles.

I am currently working on a project related to Lee-Yang zeros under the supervision of Roland Roeder at IU Indianapolis, in collaboration with a PhD student there.

I am also conducting my senior thesis on the Dyson Hierarchical Model. In addition, my research projects and reading under Professor Ilia Binder at the University of Toronto can be viewed as an initial step toward my interest in Hilbert’s sixth problem.

Honors & Awards

Connaught International Scholarship for Doctoral Students, University of Toronto, 2026-

Links

I enjoy writing random things!

Fermat’s Last Theorem for Polynomials

Solutions to some exercises (textbook: Fractals in Probability and Analysis. Note that after Chapter 1, it is much more well-written. I will no longer update this file, since these exercises can now be solved quite easily by AI.)

Supplement to Ruelle’s Proof about Extention of Lee-Yang Theorem

My Email (Please feel free to contact me!)

yapeng dot zhao at mail dot utoronto dot ca