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Caltech
Division of Physics, Mathematics and Astronomy

Tony Yue Yu

Tony Yue Yu

Professor of Mathematics
B.A., Peking University, China and École normale supérieure Paris, 2011; M.S., École normale supérieure Paris, 2013; Ph.D., University of Paris, 2016. Professor, Caltech, 2021-.

Research Interests: Algebraic geometry, enumerative geometry, mirror symmetry, birational geometry, non-archimedean geometry, tropical geometry, derived geometry, AI & machine learning

Overview

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.

Selected Awards

  • Clay Research Fellowship
  • ERC Starting Grant, European Research Council
  • New world mathematics awards Gold Prize
  • Perrisin-Pirasset Schneider Prize
  • ICCM Best Paper Award Silver Prize

Related News

Counting Curves
Read more news

Selected Publications

For a complete publications list, see feeds.library.caltech.edu

Related Courses

Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms, 2025-26. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d.
Instructors: Conlon, Gherman, Flach, T. Yu
Ma 191 abc. Selected Topics in Mathematics. 9 units (3-0-6); first, second, third terms, 2025-26. Each term we expect to give between 0 and 6 (most often 2-3) topics courses in advanced mathematics covering an area of current research interest. These courses will be given as sections of 191. Students may register for this course multiple times even for multiple sections in a single term. The topics and instructors for each term and course descriptions will be listed on the math option website each term prior to the start of registration for that term.
Instructors: T. Yu, Pham, Zhang, Yang, Heinaevaara, Looi, Svoboda, Marcolli, El-Maazouz, Flach, Dong
Ma/CS 6/106 abc. Introduction to Discrete Mathematics. 9 units (3-0-6); first, second, third terms, 2025-26. Prerequisites: for Ma/CS 6 c, Ma/CS 6 a or Ma 5 a or instructor's permission. First term: a survey emphasizing graph theory, algorithms, and applications of algebraic structures. Graphs: paths, trees, circuits, breadth-first and depth-first searches, colorings, matchings. Enumeration techniques; formal power series; combinatorial interpretations. Topics from coding and cryptography, including Hamming codes and RSA. Second term: directed graphs; networks; combinatorial optimization; linear programming. Permutation groups; counting nonisomorphic structures. Topics from extremal graph and set theory, and partially ordered sets. Third term: syntax and semantics of propositional and first-order logic. Introduction to the Godel completeness and incompleteness theorems. Elements of computability theory and computational complexity. Discussion of the P=NP problem.
Instructors: T. Yu, Babecki, Marcolli