Professor Tony Yue YU is the pioneer of the field of non-archimedean mirror symmetry, a branch of geometry and mathematical physics. He worked out the world's first example of non-archimedean curve counting. He led long-term collaborations throughout the development of this field, resulting in numerous publications in top scientific journals, including the Annals of Mathematics.

More recently, Tony Yue YU, together with Katzarkov, Kontsevich and Pantev, they solved a longstanding major problem in algebraic geometry: the irrationality of the very general cubic fourfold, a question that had resisted all approaches for over fifty years. Their work was celebrated in a Quanta Magazine article titled "String Theory Inspires a Brilliant, Baffling New Math Proof," and has been described by colleagues as bringing techniques "from the future". Their approach brought together two previously separate communities in mathematics, and has spawned study groups and workshops around the world. Professor Tony Yue YU directed his graduate students and postdocs for the development of the key ingredients and foundations, as well as further refinements and strengthening of the result.

Since joining Caltech, Professor Tony Yue YU has also led several research projects in artificial intelligence, machine learning, and combinatorics. These efforts opened new research directions and attracted exceptional students and young researchers.