Chun-Ju (CJ) Lai (賴俊儒)

cjlai@gate.sinica.edu.tw



I've joined the Academia Sinica as an Assistant Research Fellow since Sep 2020. I was a limited term assistant professor at the University of Georgia ; a visiting postdoc fellow at the Max Planck Institute for Mathematics in Bonn, Germany. My PhD advisor is Weiqiang Wang at the University of Virginia.

My main research contribution is introducing the new notion of the quantum wreath products in a joint work with Nakano and Xiang. A quantum wreath product, roughly speaking, is a uniform construction of algebras affording Bernstein-Lustztig presentations such as variants of the affine Hecke algebras, as well as non-trivial deformations from wreath products of groups which are not necessarily Coxeter groups. Historically, the study of these algebras has been challenging, often requiring a case-by-case analysis. Our work on quantum wreath products introduces a unified framework that streamlines the study of their structure and representation theory, suggesting connections to diagrammatic presentations from the perspective of monoidal categories, metaplectic covers of p-adic groups, and affine Khovanov-Lauda-Rouquier algebras.

My other research directions are active topics in modern representation theory, all connected but spanning a range of different related areas: quantum symmetric pairs and quantum groups, highest weight categories, Lie superalgebras, modular representations for affine Lie algebras, algebraic combinatorics, and Springer theory.

I'm a Program Committee member of Number Theory and Representation Theory, NCTS . I'm an organizer of the colloquium at the Institute of Mathematics, Academia Sinica, the Basic Notion Seminar at the National Taiwan University/Academia Sinica.

CV
Articles on arXiv
Google Scholar Citation page

Experience

Academia Sinica
Assistant Research Fellow
2020 - present
Institute of Mathematics
Academia Sinica, Taiwan
Institute of Advanced Study
Summer Collaborators Program
2019
Collaborators: Mee Seong Im, Jieru Zhu, Arik Wilbert
School of Mathematics, Institute of Advanced Study
University of Georgia
LT Assistant Professor
2017 - 2020
Mentor: Dan Nakano
Department of Mathematics, University of Georgia, USA
Max Planck Institute for Mathematics in Bonn
Visiting Postdoc Fellow
2016 - 2017
Max Planck Institute for Mathematics in Bonn, Germany
University of Virginia
Doctor of Philosophy
2011 - 2016
Graduate Instructor (3 years) / Teaching Assistant (.5 year)
Adviser: Weiqiang Wang
Department of Mathematics, University of Virginia, USA
National Center of Theoretical Sciences
Research Assistant
2010 - 2011
Mentor: Shun-Jen Cheng
Mathematics Division
National Center of Theoretical Sciences, Taiwan
National Taiwan University
Bachelor of Science / Science in Engineering
2005 - 2009
Double major in Electrical Engineering / Mathematics
National Taiwan University, Taiwan

Activities

Upcoming Activities
  1. Jun 18-22, 2025, 9th International Conference on Representation Theory, Nanjing, China
  2. Sep 15-19, 2025, Pohang University of Science and Technology, South Korea
  3. Oct 20-24, 2025, Seoul National University, South Korea
  4. Dec 05-07, 2025, Conference on Algebra and Representation Theory, Beijing, China
  5. Jan 04-08, 2026, Workshop on Lie Theory, Oman
  6. Mar 24-27, 2026, University of South Alabama, Mobile, USA
  7. Mar 28-29, 2026, AMS Special Session, Savanna, USA
  8. Mar 30, 2026, University of Georgia, Athens, USA
  9. Jun 15-19, 2026, Pacific Rim Conference on Mathematics, Taiwan
  10. Jul 17-21, 2026, ICM Satelite Meeting, Charlottesville, USA
Publications

  1. S. Eu, T. Fu, C. Lai,
    On the enumeration of parking functions by leading terms,
    Advances in Applied Mathematics, 35 (2005), 392 - 406.
  2. S. Eu, T. Fu, C. Lai,
    Cycle Lemma, Parking Functions and Related ultigraphs,
    Graphs and Combinatorics, 26 (2010), 345 - 360.
  3. C. Lai,
    On Weyl modules over affine Lie algebras in prime characteristic,
    Transform. Groups, 21 (2016), 1123-1153.
  4. Z. Fan, C. Lai, Y. Li, L. Luo and W. Wang,
    Affine flag varieties and quantum symmetric pairs,
    Mem. Amer. Math. Soc., 265 (2020), no. 1285. 136 pages.
  5. C. Lai,
    Affine Quantum Symmetric Pairs: Multiplication Formulas and Canonical Bases,
    PhD dissertation (2016), 124 pages.
  6. Z. Fan, C. Lai, Y. Li, L. Luo and W. Wang,
    Affine Hecke algebras and quantum symmetric pairs,
    Mem. Amer. Math. Soc. 281 (2023), no. 1381. 108 pages.
  7. C. Lai and L. Luo,
    An elementary construction of monomial bases of quantum affine gl_n,
    J. Lond. Math. Soc. 96 (2017), 15--27.
  8. Z. Fan, C. Lai, Y. Li, L. Luo, W. Wang and H. Watanabe,
    Quantum Schur duality of affine type C with three parameters,
    Math. Res. Letters, 27 (2020), 79 --114.
  9. C. Lai and L. Luo,
    Schur algebras and quantum symmetric pairs with unequal parameters,
    Int. Math. Res. Not. 13 (2021), 10207--10259.
  10. C. Lai, D. K. Nakano and Z. Xiang,
    On q-Schur algebras corresponding to Hecke algebras of type B,
    Transform. Groups, 27 (2022), 983--1024.
  11. M. Im, C. Lai and A. Wilbert,
    Irreducible components of two-row Springer fibers and Nakajima quiver varieties,
    arXiv:1910.03010, 37 pages, unpublished manuscript.
  12. M. Im, C. Lai and A. Wilbert,
    A study of irreducible components of Springer fibers using quiver varieties,
    J. Algebra. 591 (2022), 217--248.
  13. M. Im, C. Lai and A. Wilbert,
    Irreducible components of two-row Springer fibers for all classical types,
    Proc. Amer. Math. Soc. 150 (2022), 2415--2432.
  14. C. Lai, D. K. Nakano and Z. Xiang,
    Quantum wreath products and Schur-Weyl duality I,
    Forum of Math. Sigma , 12 (2024) e108.
  15. Y. Hsu and C. Lai,
    On the Springer correspondence for wreath products,
    arxiv:2404.02846 26 pages.
  16. C. Lai and A. Minets,
    Schurification of polynomial quantum wreath products,
    arxiv:2502.02108 30 pages.
  17. C. Lai, D. K. Nakano, and A. Wilbert
    Category O for Lie superalgebras,
    arxiv:2505.17422 25 pages.

Teaching

Academia Sinica
  1. Summer 2023, NCTS Lecture series on quantum wreath products
    Notes notes.
  2. Fall 2020, Representation Theory: Mini course on Springer Fibers and Quiver Varieties
    Notes week 1, week 2, week 3, week 4, week 5.
University of Georgia
  1. Spring 2020, Accelerated Calculus III for Engineering Students (Math 2500 - 25083/38466)
  2. Spring 2020, Calculus I for Science and Engineering (Math 2250 - 24973)
  3. Fall 2019, Lie Algebras (Math 8080 - 42370)
  4. Spring 2019, Calculus I for Science and Engineering (Math 2250 - 24969/24976)
  5. Fall 2018, Topics in Algebra - Quantum Groups (Math 8030 - 38839)
  6. Spring 2018, Calculus III for Science and Engineering (Math 2270 - 25075)
  7. Fall 2017, Calculus I for Science and Engineering (Math 2250 - 15618) Fall 2017, Calculus III for Science and Engineering (Math 2270 - 25509)
University of Virginia
  1. Fall 2016, Applied Calculus II (MATH 1220-010)
  2. Fall 2015, Calculus II (MATH 1320-200)
  3. Spring 2015, Applied Calculus II (MATH 1220-006)
  4. Spring 2014, Applied Calculus II (MATH 1220-009)
  5. Fall 2013, Applied Calculus I (MATH 1210-005)
Resources

  1. AMS's MathSciNet
  2. AMS's "What is..." column
  3. The preprint trinity " arXiv , Front , and SciRate "
  4. MacTutor History of Mathematics archive
  5. Real world applications of math thread on MathOverflow
  6. M. Khovanov's Representation theory resources and references
  7. B. Boe's List of Representation Theorists
  8. T. Tao's Career advice
  9. K. Carr's An Attempt at Mapping Mathematics
  10. I. Andrus's Periodic Table of Finite Simple Groups