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 current research interests include affine Hecke algebras, quantum groups, quantum symmetric pairs, modular representation theory, quiver varieties, Springer fibers, geometric representation theory, categorifications, and algebraic combinatorics.

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. Mar 18-22, 2024, Peking University and Beijing institute of technology, Beijing, China
  2. May 1-3, 2024, Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart, SLMath (MSRI), USA
  3. May 4-5, 2024, AMS sectional meeting special session, San Francisco State, USA
  4. May 27-31, 2024, Representation Theory and Related Geometry: Progress and Prospects, University of Georgia, USA
  5. Aug 25-29, 2024, Lie Theory and Related Topics, Sichuan University, Chengdu, China
Organization
  1. Dec 1-3, 2023, Conference on Algebraic Representation Theory (CART), NCTS, Taiwan
  2. Mar 17-18, 2023, AMS Sectional, Georgia Tech, USA
  3. Sep 18, 2020 - now, Learning Seminar on Representation Theory, Academia Sinica
  4. Sep 17, 2020 - now, Colloquium, Academia Sinica
  5. Mar 11-13, 2022, AMS Sectional, University of Virginia, USA
  6. Jan 17-19, 2022, TMS Annual Meeting, Academia Sinica, Taiwan
  7. Sep 28, 2020 - 2021, Basic Notion Seminar, Academia Sinica/National Taiwan University
  8. Aug 2018 - May 2020, ​Algebra Seminar, University of Georgia
  9. Mar 13-15, 2020, AMS Sectional (canceled due to COVID), University of Virginia
  10. Jun 10-12, 2018, Southeast Lie Theory Conference X, University of Georgia
Past Visitings​
  1. Mar 20-23, 2023, University of Georgia, US
  2. Mar 18-19, 2023, Georgia Tech, US
  3. Mar 13-17, 2023, University of South Alabama, US
  4. Mar 9-12, 2023, University of Virginia, US
  5. Mar 4-8, 2023, California State University Northridge, US
  6. Mar 1-3, 2023, Loyola University Chicago, US
  7. Dec 11-23, 2022, National University of Singapore, Singapore
  8. Oct 23-29, 2022, OIST, Japan
  9. Sep 20, 2022, Uppsala University, Sweden
  10. Sep 6-8, 2022, University of Cologne, Germany
  11. Oct 18, 2021, National Chengchi University, Taiwan
  12. Nov 02, 2020, Chien Kuo Senior High School, Taiwan
  13. Mar 12-13 2020, University of Virginia, US
  14. Feb 21, 2019, National Taiwan University, Taiwan
  15. Dec 24-26, 2019, National University of Singapore, Singapore
  16. Dec 20, 2019, Academia Sinica, Taiwan
  17. Dec 23, 2019, National Tsing Hua University, Taiwan
  18. Dec 19, 2019, National Sun Yet-sen University, Taiwan
  19. Nov 9-10, 2019, AMS Sectional, UC Riverside, US
  20. May 13-15, 2019, Louisiana State University, US
  21. Jun 2-15, 2019, Summer Collaborators Program, Institute for Advanced Study
  22. Mar 15-17, 2019, AMS Sectional Meeting, Auburn University, US
  23. January 7-11, 2019, Taipei Conference in Representation Theory VI, Academia Sinica, Taiwan
  24. Dec 7, 2018 - Jan 11, 2019, Academia Sinica, Taiwan
  25. Oct 19-21, 2018, Representation Theory, Combinatorics, and Geometry, University of Virginia, US
  26. Jun 4 - 9, 2018, Summer School on Lie Theory, University of Georgia, US
  27. Jun 26 - Jul 7, 2017, Academia Sinica, Taiwan.
  28. Apr 28, 2017, Universität Bielefeld, Germany.
  29. Feb 14 - 17, 2017, Université Clermont Auvergne, France.
  30. Nov 27 - Dec 01, 2016, Newcastle University, UK.
  31. Oct 20 - 21, 2016, Emmy Noether Zentrum für Algebra, FAU Erlangen-Nürnberg, Germany.
  32. Sep 23 - 27, 2016, University at Buffalo (SUNY), New York, US
  33. Jun 08 - Aug 08, 2016, Academia Sinica, Taiwan.
Conference Talks​
  1. 2024 Jan, TMS Annual Meeting, National Chengchi University, Taiwan
  2. 2023 Aug, International Algebra Conference in the Philippines (IACP), Philippines
  3. 2023 Jun, Representation Theory of Hecke Algebras and Categorification, OIST, Japan
  4. 2023 Jan, TMS Annual Meeting, National Tsing Hua University, Taiwan
  5. 2022 Nov, Two-day Workshop on Lie Theory, Fudan University, China
  6. 2021 Nov, Conference on Algebraic Representation Theory (CART), Seoul National University, Korea
  7. Dec 2020, TMS Annual Meeting, Fu-Jen Catholic University, Taiwan
  8. Aug 2020, Taipei workshop on representation theory and related topics, Academia Sinica, Taiwan
  9. Oct 2020, AMS Sectional Meeting, University of Utah, US
  10. Nov 2019, AMS Sectional Meeting, University of California Riverside, US
  11. May 2019, Southeastern Lie Theory Workshop, Louisiana State University, US
  12. Mar 2019, AMS Sectional Meeting, Auburn University, US
  13. Oct 2018, Representation Theory, Combinatorics, and Geometry, University of Virginia, US
  14. Sep 2017, AMS Sectional Meeting, University at Buffalo (SUNY), US
  15. Jul 2017, Taipei Workshop on Representation Theory of Lie Superalgebras and Related Topics, Academia Sinica, Taiwan
  16. May 2016, Algebraic Groups, Quantum Groups and Geometry, University of Virginia, US
  17. May 2016, Workshop on Hecke Algebras and Lie Theory, University of Ottawa, Canada
  18. May 2015, Southeastern Lie Theory Workshop, North Carolina State University, US
  19. Jun 2015, Workshop on Lie Theory and Representation Theory, East China Normal University, China
  20. Mar 2015, AMS Sectional Meeting, Georgetown University, US
  21. May 2014, Southeastern Lie Theory Workshop, University of Georgia, US
  22. Jul 2010, Cross-strait Conference on Graph Theory and Combinatorics, National Taiwan University, Taiwan
Seminar Talks and Mini Courses
  1. Nov 22, 2023, Algebra Seminar, SUSTech, China
  2. Oct 26, 2023, Colloquium, Central University, Taiwan
  3. Mar 20, 2023, Algebra Seminar, University of Georgia, USA
  4. Mar 10, 2023, Algebra Seminar, University of Virginia, USA
  5. Mar 06, 2023, Algebra Seminar, California State University Northridge, USA
  6. Mar 01, 2023, TACO Seminar, Loyola University Chicago, USA
  7. Nov 01, 2022, Representation Theory Seminar, OIST, Japan
  8. Oct 18, 2022, Algebra Seminar, University of Cologne, Germany
  9. Oct 14, 2022, ”What are you thinking about?” Seminar, University of Amsterdam, Netherlands
  10. Sep 20, 2022, Algebra Seminar, Uppsala University, Sweden
  11. Mar 21, 2022, Awardee Lecture, NCTS, Taiwan
  12. Mar 16, 2022, Algebra Seminar, University of Virginia
  13. Mar 3, 2022, Colloquium, National Cheng Kung University, Taiwan
  14. Mar 1, 2022, Algebra Seminar, University of Georgia
  15. Feb 21, 2022, Colloquium, National Taiwan University, Taiwan
  16. Oct 18, 2021, Colloquium, National Chengchi University, Taiwan
  17. Sep 30, 2021, QSMS Seminar, Center for Quantum Structures in Modules and Spaces, Korea
  18. May 03, 2021, Colloquium, National Tsing Hua University, Taiwan
  19. Jan 07, 2021, Colloquium, National Central University, Taiwan
  20. Dec 17, 2020, Algebra Seminar, National Cheng Kung University, Taiwan
  21. Dec 5 - 6, 2020, TMS Annual Meeting (invited), Fu-Jen Catholic University, Taiwan
  22. Nov 19, 2020, Algebra Seminar, Jagiellonian University, Poland
  23. Nov 09, 2020, Basic Notions Seminar, National Taiwan University, Taiwan
  24. Oct 16 - Nov 14, 2020, Minicourse on representation theory, National Center of Theoretical Sciences, Taiwan
  25. Aug 31 - Sep 2, 2020, Taipei workshop on representation theory and related topics (invited), Academia Sinica, Taiwan
  26. Oct 28, 2019, Algebra Seminar, Irreducible components of two-row Springer fibers and Nakajima's quiver varieties, University of Georgia
  27. Jan 28, 2019, Algebra Seminar, On q-Schur algebras of type B via coordinate coalgebras, University of Georgia
  28. Jan 03, 2019, Seminar, Constructing q-Schur algebras of type B via coordinate coalgebras, Academia Sinica, Taiwan
  29. Sep 03, 2018, Algebra Seminar, Master Schur Duality, University of Georgia
  30. Apr 02, 2018, Algebra Seminar, Weyl modules over affine Lie algebras in prime characteristic, University of Georgia
  31. Sep 25, 2017, Algebra Seminar, Quantum groups arising from Schur-type dualities II, University of Georgia
  32. Aug 30, 2017, Oberseminar, From Schur duality to quantum symmetric pairs, University of Georgia
  33. Aug 28, 2017, Algebra Seminar, Quantum groups arising from Schur-type dualities I, University of Georgia
  34. Apr 28, 2017, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Universität Bielefeld, Germany
  35. Feb 17, 2017, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Université Clermont Auvergne
  36. Dec 16, 2016, Oberseminar Representation Theory, Affine Hecke algebras and quantum symmetric pairs, Universität Bonn, Germany.
  37. Dec 12, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, IMJ-PRG, France.
  38. Dec 8, 2016, MPI-Oberseminar, From Schur duality to quantum symmetric pairs, MPIM Bonn, Germany.
  39. Nov 29, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Newcastle University.
  40. Oct 21, 2016, Emmy Noether Seminar, Affine Hecke algebras and quantum symmetric pairs, Emmy Noether Center, FAU Erlangen-Nürnberg.
  41. Sep 25, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, University at Buffalo, SUNY.
  42. Jul 2016, Mini course: Fifty shades of quantum groups, National Taiwan Normal University, Taiwan.
  43. Dec 2015, Lie Group/Representation Theory Seminar, Affine flag varieties, Hecke algebras, and quantum symmetric pairs, University of Maryland.
  44. Nov 2015, Algebra seminar, Quantum symmetric pairs of affine type: multiplication formulas, canonical bases, and Schur dualities, University of Virginia.
  45. Dec 2014, Seminar, An elementary approach to monomial and canonical bases of quantum affine gl_n, Academia Sinica, Taiwan.
  46. Dec 2014, Mini course on representation theory of Lie algebras, National Central University, Taiwan.
  47. Dec 2014, Seminar, Quantum groups and q-Schur dualities, National Central University, Taiwan.
  48. Jul 2014, Mini course on representation theory of Lie algebras, National Taiwan Normal University, Taiwan.
  49. May 2014, Algebra seminar, Quantum Schur-type dualities of finite and affine type B, University of Virginia.
  50. Nov 2013, Graduate seminar, I park my car in a Weyl alcove by a labeled tree, University of Virginia.
  51. Sep 2013, Algebra seminar, On Weyl modules over affine Lie algebras in prime characteristic, University of Virginia.
  52. Nov 2010, Seminar, Algorithms on parking functions and related multigraphs, National University of Kaohsiung, Taiwan.
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,
    arxiv.org/abs/2304.14181, 31 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