Undergraduate Research

  • Henghui Li @ University of Virginia
    Project: A note on the center of twisted Yangians

Mentoring

  • 2024 Spring, Directed Reading Program @ University of Virginia
    Mentee: Henghui Li
    Reading Project: Representation Theory and Symmetric Functions

  • 2023 Fall, Directed Reading Program @ University of Virginia
    Mentee: Alex Ning
    Reading project: Convex Optimization and Support Vector Machine

Journal Referee

  • Algebras and Representation Theory
  • Arnold Mathematical Journal
  • Communications in Mathematical Physics
  • Compositio Mathematica
  • Journal of Algebra
  • Journal of Mathematical Physics
  • Journal de l’École polytechnique - Mathématiques
  • Letters in Mathematical Physics
  • Pacific Journal of Mathematics
  • SciPost Physics
  • Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
  • Transformation Groups

Local service and outreach

General Information

Information
Instructor Kang Lu (wbt4qn) at Kerchof Hall 229
Office Hours Wednesdays 2:00-3:15pm and Thursdays 12:30-1:30pm
TA Suren Kyurumyan (yyk2hk) at Kerchof Hall 112
TA Office Hours Wednesdays 11:00-12:00pm
Mid-Term 1 February 22, 2024
Mid-Term 2 April 04, 2024
Final Exam 9:00am - 12:00pm May 10, 2024 for Session 100 and May 3, 2024 for Session 200
Syllabus   Syllabus S100   Syllabus S200

All exams are in class. I will use different exams for different sessions.

Textbooks

The text is James Stewart’s Multivariable Calculus, 9th edition, Cengage Learning.

Earlier editions of this text differ in some sections and most exercises.

Course Documents

  • Some commonly used blackboard/homework short hand notation.
  • How to write up problem-sets and exams? Please read the solution guide.
  • For more applications of vector calculus in physics, please see the notes by Miki Havlickova and Michael Frame from Yale University on electric and magnetic fields and Maxwell’s equations.

Homeworks

Homeworks are assigned on WebAssign and GradeScope. The class key for signing up WebAssign will be given at the beginning of the semester.

Quizzes and Exams

  Sample Midterm   Practice Final Exam

Lecture Notes

Dates Lecture Notes Quiz/Exam
01/18   Chapter 12.2   Chapter 12.3
01/23   Chapter 12.4
01/25   Chapter 12.5   Quiz 1 Solution
01/30   Chapter 13.1   Chapter 13.2   Chapter 13.3
02/01   Chapter 13.4   Chapter 14.1   Quiz 2 Solution
02/06   Chapter 14.2
02/08   Chapter 14.3   Quiz 3 Solution
02/13   Chapter 14.4
02/15   Chapter 14.5   Quiz 4 Solution
02/20   Chapter 14.6
02/22   Midterm 1 Solution
02/27   Chapter 14.7   Chapter 15.1A
02/29   Chapter 15.1B   Chapter 15.2   Quiz 5 Solution
03/12   Chapter 15.3
03/14   Chapter 16.1   Quiz 6 Solution
03/19   Chapter 16.2
03/21   Chapter 16.3   Quiz 7 Solution
03/26   Chapter 16.4
03/28   Chapter 16.5   Quiz 8 Solution

Personal Information

I am a research associate and lecturer at University of Virginia, mentored by Weiqiang Wang. Before that I was a Visiting Assistant Professor at University of Denver and my mentor was Andrew Linshaw. I received my Ph.D. in Mathematics from Indiana University Purdue University Indianapolis (IUPUI), advised by Evgeny Mukhin and Vitaly Tarasov.

  • Email: Kang$\cdot$Lu@Virginia$\cdot$edu, Kang$\cdot$Lu$\cdot$math@gmail$\cdot$com
  • Address: Kerchof Hall 229, 141 Cabell Drive, Charlottesville, VA 22904
  •   My CV

Education

Research Interests

Generally speaking, I am interested in Representation Theory and Quantum Algebras.

More specifically, my current research interests are: Representation Theory of Quantum Groups, Lie Algebras and Superalgebras, and Integrable System.

Preprints

See also arXiv

  1. A class of representations for twisted Yangians and affine $\imath$quantum groups
    (with Weiqiang Wang), in preparation
  2. A Drinfeld type presentation of twisted Yangians of quasi-split ADE type
    (with Weinan Zhang), in preparation
  3. A Drinfeld type presentation of twisted Yangians via degeneration
    (with Weiqiang Wang and Weinan Zhang), in preparation
  4. Twisted super Yangians of type AIII and their representations
    (arXiv:2311.16373)   Updated on 03/04/2024
  5. Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI
    (arXiv:2308.12484)
  6. A Drinfeld type presentation of twisted Yangians
    (with Weiqiang Wang and Weinan Zhang), (arXiv:2308.12254)

Publications

See also MathSciNet.

  1. On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
    Journal of High Energy Physics 04 (2023), Article number: 120, (arXiv:2209.14416)
  2. Schur-Weyl duality for quantum toroidal superalgebras
    Journal of Pure and Applied Algebra 227 (2023), no. 9, 107382, (arXiv:2109.09005)
  3. Completeness of Bethe ansatz for Gaudin models associated with $\mathfrak{gl}(1|1)$
    Nuclear Physics B 980 (2022), Paper No. 115790, 23 pp (arXiv:2202.08162)
  4. A note on odd reflections of super Yangian and Bethe ansatz
    Letters in Mathematical Physics 112 (2022), Article no.: 29 (arXiv:2111.10655)
  5. Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
    Letters in Mathematical Physics 111 (2021), Article no.: 145 (arXiv:2103.08758).
  6. Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces (with E. Mukhin)
    Annales Henri Poincaré 22 (2021), 4087–4130, (arXiv:2103.16729).
  7. On the supersymmetric XXX spin chains associated to $\mathfrak{gl}_{1|1}$ (with E. Mukhin)
    Communications in Mathematical Physics 386 (2021), 711–747, (arXiv:1910.13360).
  8. Jacobi-Trudi identity and Drinfeld functor for super Yangian (with E. Mukhin)
    International Mathematics Research Notices 2021 (2021), no. 21, 16749–16808, (arXiv:2007.15573).
  9. Perfect integrability and Gaudin models
    Symmetry, Integrability and Geometry: Methods and Applications 16 (2020), 132, 10 pages, (arXiv:2008.06825).
  10. Solutions of \(\mathfrak{gl}_{m|n}\) XXX Bethe ansatz equation and rational difference operators (with Chenliang Huang, E. Mukhin)
    Journal of Physics A: Mathematical and Theoretical 52 (2019) 375204 (31pp), (arXiv:1811.11225)
  11. On the Gaudin model of type \(G_2\) (with E. Mukhin)
    Communications in Contemporary Mathematics 21 (2019), no. 3, 1850012, 31 pages, (arXiv:1711.02511)
  12. Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root systems (with Gang Han, Yucheng Liu)
    Algebra Colloquium 26 (2019), no. 1, 123-138, (arXiv:1611.03943)
  13. Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
    Symmetry, Integrability and Geometry: Methods and Applications 14 (2018), 046, 15 pages, (arXiv:1710.06534)
  14. Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\) (with E. Mukhin, A. Varchenko)
    Pure and Applied Mathematics Quarterly 13 (2017), no.2, 291 – 335 , a special issue of in honor of Yuri Manin’s 80-th birthday, (arXiv:1705.02048)
  15. On the Gaudin model associated to Lie algebras of classical types (with E. Mukhin, A. Varchenko)
    Journal of Mathematical Physics 57 (2016), 101703, 23 pages (arXiv:1512.08524)

Research Interests

Generally speaking, I am interested in Representation Theory and Quantum Algebras.

More specifically, my current research interests are: Bethe ansatz method, Representation Theory of Quantum Groups, Lie Algebras and Superalgebras, and Integrable System.

Preprints

See also arXiv

  1. A Drinfeld type Presentation of twisted Yangians
    (with Weiqiang Wang and Weinan Zhang), in preparation

Publications

See also MathSciNet.

  1. On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
    J. High Energ. Phys. 04, Article number: 120 (2023), (arXiv:2209.14416)
  2. Schur-Weyl duality for quantum toroidal superalgebras
    J. Pure Appl. Algebra 227 (2023), no. 9, 107382, (arXiv:2109.09005)
  3. Completeness of Bethe ansatz for Gaudin models associated with $\mathfrak{gl}(1|1)$
    Nuclear Phys. B 980 (2022), Paper No. 115790, 23 pp (arXiv:2202.08162)
  4. A note on odd reflections of super Yangian and Bethe ansatz
    Lett. Math. Phys. 112 (2022), Article no.: 29 (arXiv:2111.10655)
  5. Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
    Lett. Math. Phys. 111 (2021), Article no.: 145 (arXiv:2103.08758).
  6. Bethe ansatz equations for orthosymplectic Lie superalgebra and self-dual superspaces
    (with E. Mukhin), Annales Henri Poincaré 22 (2021), 4087–4130 , (arXiv:2103.16729).
  7. On the supersymmetric XXX spin chains associated to $\mathfrak{gl}_{1|1}$
    (with E. Mukhin), Commun. Math. Phys. 386 (2021), 711–747, (arXiv:1910.13360).
  8. Jacobi-Trudi identity and Drinfeld functor for super Yangian
    (with E. Mukhin), Int. Math. Res. Not. IMRN 2021 (2021), no. 21, 16749–16808, (arXiv:2007.15573).
  9. Perfect integrability and Gaudin models
    SIGMA 16 (2020), 132, 10 pages, (arXiv:2008.06825).
  10. Solutions of \(\mathfrak{gl}_{m|n}\) XXX Bethe ansatz equation and rational difference operators
    (with Chenliang Huang, E. Mukhin), J. Phys. A: Math. Theor. 52 (2019) 375204 (31pp), (arXiv:1811.11225)
  11. On the Gaudin model of type \(G_2\)
    (with E. Mukhin), Commun. Contemp. Math. 21 (2019), no. 3, 1850012, 31 pages, (arXiv:1711.02511)
  12. Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root systems
    (with Gang Han, Yucheng Liu), Algebra Colloq. 26 (2019), no. 1, 123-138, (arXiv:1611.03943)
  13. Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus
    SIGMA 14 (2018), 046, 15 pages, (arXiv:1710.06534)
  14. Self-dual Grassmannian, Wronski map, and representations of \(\mathfrak{gl}_N\), \(\mathfrak{sp}_{2r}\), \(\mathfrak{so}_{2r+1}\)
    (with E. Mukhin, A. Varchenko), Pure Appl. Math. Q. 13 (2017), no.2, 291 – 335 , a special issue of in honor of Yuri Manin’s 80-th birthday, (arXiv:1705.02048)
  15. On the Gaudin model associated to Lie algebras of classical types
    (with E. Mukhin, A. Varchenko), J. Math. Phys. 57 (2016), 101703, 23 pages (arXiv:1512.08524)

Collaborators

My Erdös Number: 4.
Paul Erdős–>Shizuo Kakutani–>Karl Endel Petersen–>A. N. Varchenko–>Kang Lu

University of Virginia

University of Denver

  • MATH 1952: Calculus II, 2022 Summer
  • MATH 2070: Introduction to Differential Equations, 2022 Spring
  • MATH 2080: Calculus of Several Variables, 2022 Spring
  • MATH 1951: Calculus I, 2022 Winter
  • MATH 1150: Mathematics for Cryptography, 2022 Winter
  • MATH 1951: Calculus I, 2021 Autumn
  • MATH 1952: Calculus II, 2020 Spring
  • MATH 1150: Introduction to Cryptography, 2020 Winter
  • MATH 2070: Introduction to Differential Equations, 2020 Winter
  • MATH 1951: Calculus I, 2020 Autumn

IUPUI

  • MATH 16500: Analytic Geometry and Calculus I, 2020 Summer I
  • MATH 15300: College Algebra, 2020 Spring
  • MATH 22100: Calculus for Technology I, 2020 Spring
  • MATH 15400: Trigonometry, 2019 Fall (2 sessions)
  • MATH 26600: Ordinary Differential Equations, 2019 Summer II
  • MATH 22100: Calculus for Technology I, 2019 Spring
  • MATH 11100: Intermediate Algebra, 2018 Fall
  • MATH 15400: Trigonometry, 2018 Summer II
  • MATH 11000: Fundamentals of Algebra, 2018 Spring
  • MATH 16500: Integrated Calculus and Analytic Geometry I, 2017 Fall (recitation, 2 sessions)

Upcoming travels

Past travels

2023

Before 2023

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