Assistant Research Fellow
2020 - present
Institute of Mathematics
Academia Sinica, Taiwan
Summer Collaborators Program
2019
Collaborators: Mee Seong Im, Jieru Zhu, Arik Wilbert
School of Mathematics, Institute of Advanced Study
LT Assistant Professor
2017 - 2020
Mentor: Dan Nakano
Department of Mathematics,
University of Georgia, USA
Visiting Postdoc Fellow
2016 - 2017
Max Planck Institute for Mathematics in Bonn, Germany
Doctor of Philosophy
2011 - 2016 Graduate Instructor (3 years) / Teaching Assistant (.5 year)
Adviser: Weiqiang Wang
Department of Mathematics, University of Virginia, USA
Research Assistant
2010 - 2011
Mentor: Shun-Jen Cheng
Mathematics Division
National Center of Theoretical Sciences, Taiwan
Bachelor of Science / Science in Engineering
2005 - 2009
Double major in Electrical Engineering / Mathematics
National Taiwan University, Taiwan
Activities
Upcoming Activities
Mar 18-22, 2024,
Peking University and Beijing institute of technology, Beijing, China
May 1-3, 2024,
Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart, SLMath (MSRI), USA
May 4-5, 2024,
AMS sectional meeting special session, San Francisco State, USA
May 27-31, 2024,
Representation Theory and Related Geometry: Progress and Prospects, University of Georgia, USA
Aug 25-29, 2024,
Lie Theory and Related Topics, Sichuan University, Chengdu, China
Organization
Dec 1-3, 2023, Conference on Algebraic Representation Theory (CART), NCTS, Taiwan
Nov 19, 2020, Algebra Seminar, Jagiellonian University, Poland
Nov 09, 2020, Basic Notions Seminar, National Taiwan University, Taiwan
Oct 16 - Nov 14, 2020,
Minicourse on representation theory,
National Center of Theoretical Sciences, Taiwan
Aug 31 - Sep 2, 2020, Taipei workshop on representation theory and related topics (invited), Academia Sinica, Taiwan
Oct 28, 2019, Algebra Seminar, Irreducible components of two-row Springer fibers and Nakajima's quiver varieties, University of Georgia
Jan 28, 2019, Algebra Seminar, On q-Schur algebras of type B via coordinate coalgebras, University of Georgia
Jan 03, 2019, Seminar, Constructing q-Schur algebras of type B via coordinate coalgebras, Academia Sinica, Taiwan
Sep 03, 2018, Algebra Seminar, Master Schur Duality, University of Georgia
Apr 02, 2018, Algebra Seminar, Weyl modules over affine Lie algebras in prime characteristic, University of Georgia
Sep 25, 2017, Algebra Seminar, Quantum groups arising from Schur-type dualities II, University of Georgia
Aug 30, 2017, Oberseminar, From Schur duality to quantum symmetric pairs, University of Georgia
Aug 28, 2017, Algebra Seminar, Quantum groups arising from Schur-type dualities I, University of Georgia
Apr 28, 2017, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Universität Bielefeld, Germany
Feb 17, 2017, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Université Clermont Auvergne
Dec 16, 2016, Oberseminar Representation Theory, Affine Hecke algebras and quantum symmetric pairs, Universität Bonn, Germany.
Dec 12, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, IMJ-PRG, France.
Dec 8, 2016, MPI-Oberseminar, From Schur duality to quantum symmetric pairs, MPIM Bonn, Germany.
Nov 29, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, Newcastle University.
Oct 21, 2016, Emmy Noether Seminar, Affine Hecke algebras and quantum symmetric pairs, Emmy Noether Center, FAU Erlangen-Nürnberg.
Sep 25, 2016, Algebra Seminar, Affine Hecke algebras and quantum symmetric pairs, University at Buffalo, SUNY.
Jul 2016, Mini course: Fifty shades of quantum groups, National Taiwan Normal University, Taiwan.
Dec 2015, Lie Group/Representation Theory Seminar, Affine flag varieties, Hecke algebras, and quantum symmetric pairs, University of Maryland.
Nov 2015, Algebra seminar, Quantum symmetric pairs of affine type: multiplication formulas, canonical bases, and Schur dualities, University of Virginia.
Dec 2014, Seminar, An elementary approach to monomial and canonical bases of quantum affine gl_n, Academia Sinica, Taiwan.
Dec 2014, Mini course on representation theory of Lie algebras, National Central University, Taiwan.
Dec 2014, Seminar, Quantum groups and q-Schur dualities, National Central University, Taiwan.
Jul 2014, Mini course on representation theory of Lie algebras, National Taiwan Normal University, Taiwan.
May 2014, Algebra seminar, Quantum Schur-type dualities of finite and affine type B, University of Virginia.
Nov 2013, Graduate seminar, I park my car in a Weyl alcove by a labeled tree, University of Virginia.
Sep 2013, Algebra seminar, On Weyl modules over affine Lie algebras in prime characteristic, University of Virginia.
Nov 2010, Seminar, Algorithms on parking functions and related multigraphs, National University of Kaohsiung, Taiwan.
Publications
S. Eu, T. Fu, C. Lai,
On the enumeration of parking functions by leading terms, Advances in Applied Mathematics,
35 (2005), 392 - 406.
S. Eu, T. Fu, C. Lai,
Cycle Lemma, Parking Functions and Related ultigraphs, Graphs and Combinatorics,
26 (2010), 345 - 360.
C. Lai,
On Weyl modules over affine Lie algebras in prime characteristic, Transform. Groups, 21 (2016), 1123-1153.
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.
C. Lai,
Affine Quantum Symmetric Pairs: Multiplication Formulas and Canonical Bases,
PhD dissertation (2016), 124 pages.
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.
C. Lai and L. Luo,
An elementary construction of monomial bases of quantum affine gl_n, J. Lond. Math. Soc. 96 (2017), 15--27.
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.
C. Lai and L. Luo,
Schur algebras and quantum symmetric pairs with unequal parameters, Int. Math. Res. Not. 13 (2021), 10207--10259.
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.
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.
M. Im, C. Lai and A. Wilbert,
A study of irreducible components of Springer fibers using quiver varieties, J. Algebra. 591 (2022), 217--248.
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.
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
Summer 2023, NCTS Lecture series on quantum wreath products
Notes
notes.
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
Spring 2020, Accelerated Calculus III for Engineering Students (Math 2500 - 25083/38466)
Spring 2020, Calculus I for Science and Engineering (Math 2250 - 24973)
Fall 2019, Lie Algebras (Math 8080 - 42370)
Spring 2019, Calculus I for Science and Engineering (Math 2250 - 24969/24976)
Fall 2018, Topics in Algebra - Quantum Groups (Math 8030 - 38839)
Spring 2018, Calculus III for Science and Engineering (Math 2270 - 25075)
Fall 2017, Calculus I for Science and Engineering (Math 2250 - 15618)
Fall 2017, Calculus III for Science and Engineering (Math 2270 - 25509)