Sangjib Kim

Professor of Mathematics
sk23 (at) korea. ac. kr

Department of Mathematics
Korea University
Asan Science Hall 514
145 Anam-ro Seongbuk-gu
Seoul 02841, South Korea


Research interests

Representation theory, invariant theory, and algebraic combinatorics.
I also enjoy good collaborations with researchers in other fields of science.

Education

  • Ph.D., Yale University 2005 under the supervision of Roger Howe
  • B.Sc., Korea University 1998 with highest honors

Employment

  • Korea University, Department of Mathematics, Seoul, Korea
    Professor (9.2019-present), Associate Professor (9.2015-8.2019)

  • Ewha Women's University, Department of Mathematics, Seoul, Korea
    Associate Professor (3.2014-8.2015), Assistant Professor (3.2013-2.2014)

  • the University of Queensland, Brisbane QLD, Australia
    School of Mathematics and Physics, Lecturer (1.2011-1.2013)

  • Tata Institute of Fundamental Research, Mumbai, Maharashtra, India
    School of Mathematics, Visiting Fellow (9.2010-12.2010)

  • the University of Arizona, Tucson AZ, USA
    Department of Mathematics, Visiting Assistant Professor (8.2008-5.2010)

  • Cornell University, Ithaca NY, USA
    Department of Mathematics, Visiting Assistant Professor (8.2007-8.2008)

  • the National University of Singapore, Singapore
    Department of Mathematics, Visiting Fellow (7.2005-7.2007)


KU undergraduate math

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Publication

  • Hodge dual operators and model algebras for rational representations of the general linear group (with Soo Teck Lee)
    Journal of Algebra, 562 (2020), 497-536.

  • Standard bases for tensor products of exterior powers (with Roger Howe and Soo Teck Lee)
    Algebras and Representation Theory, 23 (2020), no. 3, 715-738.

  • On the structures of hive algebras and tensor product algebras for general linear groups of low rank (with Donggyun Kim and Euisung Park)
    International Journal of Algebra and Computation 29 (2019), no. 7, 1193-1218.

  • Hibi algebras and representation theory (with Victor Protsak)
    Acta Mathematica Vietnamica 44 (2019), no. 1, 307-323.
    Special Issue: The Prospects for Commutative Algebra, Osaka 2017.

  • Skew Pieri algebras of the general linear group (with Soo Teck Lee and Yi Wang)
    Journal of Mathematical Physics 59 (2018), no. 12, 121702, 13 pp.

  • A presentation of the double Pieri algebra
    Journal of Pure and Applied Algebra 222 (2018), no. 2, 368-381.

  • Double Pieri algebras and iterated Pieri algebras for the classical groups (with Roger Howe and Soo Teck Lee)
    American Journal of Mathematics 139 (2017), no. 2, 347-401.

  • Standard monomial theory for harmonics in classical invariant theory (with Roger Howe and Soo Teck Lee)
    Representation Theory, Number Theory and Invariant Theory - Howe 70 Conference, 265-302.
    Progress in Mathematics 323, Birkähuser/Springer, New York, 2017.

  • A specific groove pattern can effectively induce osteoblast differentiation (with C.S. Kim et al.)
    Advanced Functional Materials, Volume 27, Issue 44, November 24, 2017.

  • Pieri and Littlewood-Richardson rules for two rows and cluster algebra structure (with Semin Yoo)
    Journal of Algebraic Combinatorics 45 (2017), no. 3, 887-909.

  • The Littlewood-Richardson rule and Gelfand-Tsetlin patterns (with Patrick Doolan)
    Algebra and Discrete Mathematics 22 (2016), no. 1, 21-47.

  • Standard monomial theory of RR varieties (with Philip Foth)
    Algebra Colloquium 22 (2015), no. 3, 395-404.

  • Row convex tableaux and Bott-Samelson varieties (with Philip Foth)
    Journal of Australian Mathematical Society 97 (2014), no. 3, 315-330.

  • Tiling branching multiplicity spaces with GL2 pattern blocks
    Journal of Australian Mathematical Society 94 (2013), no. 3, 362-374.

  • Pieri algebras for the orthogonal and symplectic groups (with Soo Teck Lee)
    Israel Journal of Mathematics 195 (2013), no. 1, 215-245.

  • Quivers, invariants and quotient correspondence (with Yi Hu)
    Journal of Algebra 393 (2013), 197-216.

  • Distributive lattices, affine semigroups, and branching rules of the classical groups
    Journal of Combinatorial Theory Series A 119 (2012), no. 6, 1132-1157.

  • A basis for the symplectic group branching algebra (with Oded Yacobi)
    Journal of Algebraic Combinatorics 35 (2012), no. 2, 269-290.

  • The nullcone in the multi-vector representation of the symplectic group and related combinatorics
    Journal of Combinatorial Theory Series A 117 (2010), no. 8, 1231-1247.

  • On Kostant's partial order on hyperbolic elements (with Huajun Huang)
    Linear Multilinear Algebra 58 (2010), no. 5-6, 783-788

  • Standard monomial bases and degenerations of SOm(C) representations
    Journal of Algebra 322 (2009), no. 11, 3896-3911.

  • Standard monomial theory for flag algebras of GL(n) and Sp(2n)
    Journal of Algebra 320 (2008), no. 2, 534-568.


Student Supervision

  • 서해윤HaeYun Seo (KU M.Sc., Aug 2018)
    Filtrations on the ring of Laurent polynomials and the general linear Lie algebra

  • 최천호Cheonho Choi (KU M.Sc., Feb 2018)
    On rank 2 semisimple Lie algebras

  • 유세민Semin Yoo (EWU M.Sc., June 2016)
    Cluster algebra structure of certain quadratic algebras

  • Patrick Doolan (UQ Honours, 2012)
    Young tableaux, noncrossing diagrams and invariant theory

  • Daniel Pietrobon (UQ Honours, 2012)
    Enumeration of paths, plane partitions and tableaux

  • Patrick Doolan (UQ Advanced Study in Science, 2011)
    Combinatorics of the Littlewood-Richardson rule


Teaching

  • Korea University
    MTH801: Research in Algebra I: Classical Groups
    MTH707: Lie Groups and Lie Algebras
    MTH701: Representation Theory of Groups
    MTH501: Graduate Algebra I
    Math469: Topics in Algebra
    Math464: Combinatorics
    Math321, 362: Abstract Algebra I, II
    Math240: Differential Equations
    Math221, 222: Linear Algebra I, II
    Math203: Discrete Mathematics
    Math161, 162: Calculus I, II

  • Ewha Women's University
    Representation Theory (with JH Lee) (Semester 2/2014)
    Topics in Algebra (with JH Lee) (Semester 1/2014)
    Algebra II (Semester 2/2013)
    Linear Algebra I, II (Semester 1/2013-1/2015)
    Calculus I, II (Semester 1/2013-1/2015)

  • the University of Queensland
    Math4304/7304: Number Theory (with Victor Scharaschkin) (Semester 2/2012)
    Math3303/7333: Abstract Algebra & Number Theory (Semester 1/2011, 1/2012)
    Math1061/7861: Discrete Mathematics (Semester 2/2011, 2/2012)

  • the University of Arizona
    Math215: Introduction to Linear Algebra (Spring 2010)
    Math124: Calculus I with Applications (Fall 2008, Fall 2009)
    Math125: Calculus I (Spring 2009)

  • Cornell Univeristy
    Math323: Introduction to Differential Equations (Fall 2007)
    Math221: Linear Algebra (Fall 2007)
    Math112: Calculus II (Spring 2008)

  • the National University of Singapore
    Math6221: Introduction to Algebraic Combinatorics (Spring 2006)

  • Yale University
    Math112, 115, 120: (Fall 2001 - Spring 2005)
    Single variable Calculus I and II, Multivariable Calculus