Associate Professor

Biography

Prof. Ip is currently an Associate Professor in the HKUST Department of Mathematics. He joined HKUST as an Assistant Professor in June 2018. Prior to his appointment in HKUST, he stayed in Japan for 6 years as an Assistant Professor at Kyoto University from 2015-2018, and a Project Researcher at Kavli IPMU, Tokyo University from 2012-2015. He grew up in Hong Kong and was an IMO Medalist for the Hong Kong team in 2002. He received his B.Sc. in Mathematics and Physics from HKUST, and his Ph.D. in Mathematics from Yale University under the supervision of Igor Frenkel.

Research Interests

Representation Theory, Quantum Groups, Cluster Algebra, Integrable Systems

Teaching

• MATH4991  Capstone Project in Pure Mathematics
• MATH6912Y  Reading Course: Poisson Geometry and Hamiltonian Reduction

Selected Publications

  Article

1. On the polynomiality conjecture of cluster realization of quantum groups
   • Author(s): Ip, Ivan Chi Ho; Ye, Jeff York
   • Source: Journal of Algebra, v. 663, February 2025, p. 119-149
   • Year: 2025


2. Positive Representations with Zero Casimirs
   • Author(s): Ip, Ivan Chi-Ho; Man, Ryuichi
   • Source: Communications in Mathematical Physics, v. 405, (4), April 2024, article number 91
   • Year: 2024


3. On tensor product decomposition of positive representations of U _qq^~(sl(2, R))
   • Author(s): Ip, Ivan Chi Ho
   • Source: Letters in Mathematical Physics, v. 111, (2), April 2021, article number 39
   • Year: 2021


4. Positive Representations of Split Real Simply-Laced Quantum Groups
   • Author(s): Ip, Ivan Chi Ho
   • Source: Publications of the Research Institute for Mathematical Sciences, v. 56, (3), 17 June 2020, p. 603-646
   • Year: 2020


5. Cluster Realization of Positive Representations of a Split Real Quantum Borel Subalgebra
   • Author(s): Ip, Ivan Chi Ho
   • Source: Theoretical and Mathematical Physics(Russian Federation), v. 198, (2), February 2019, p. 215-238
   • Year: 2019


6. On Ramond Decorations
   • Author(s): Ip, Ivan Chi Ho; Penner, Robert Clark; Zeitlin, Anton M.
   • Source: Communications In Mathematical Physics, v. 371, (1), October 2019, p. 145-157
   • Year: 2019


7. On Tensor Products of Positive Representations of Split Real Quantum Borel Subalgebra U_qq (b_ℝ)
   • Author(s): Ip, Ivan Chi Ho
   • Source: Transactions of the American Mathematical Society, v. 370, (6), June 2018, p. 4177-4200
   • Year: 2018


8. N=2 super-Teichmuller theory
   • Author(s): Ip, Ivan Chi Ho; Robert C. Penner; Anton M. Zeitlin
   • Source: Advances in Mathematics, v. 336, October 2018, p. 409-454
   • Year: 2018


9. Cluster Realization of U_q(g) and Factorizations of The Universal R-matrix
   • Author(s): Ip, Ivan Chi Ho
   • Source: Selecta Mathematica, New Series, v. 24, (5), November 2018, p. 4461-4553
   • Year: 2018


10. Quantum Dilogarithm Identities at Root of Unity
    • Author(s): Ip, Ivan Chi Ho; Yamazaki, M.
    • Source: International Mathematics Research Notices, v. 2016, (3), 2016, p. 669-695
    • Year: 2016


11. Positive Casimir and Central Characters of Split Real Quantum Groups
    • Author(s): Ip, Ivan Chi Ho
    • Source: Communications in Mathematical Physics, v. 344, (3), June 2016, p. 857-888
    • Year: 2016


12. Gauss-lusztig Decomposition for Positive Quantum Groups and Representation by Q-tori
    • Author(s): Ip, Ivan Chi Ho
    • Source: Journal of Pure and Applied Algebra, v. 219, (12), December 2015, p. 5650-5672
    • Year: 2015


13. Positive Representations of Split Real Quantum Groups: The Universal R Operator
    • Author(s): Ip, Ivan Chi Ho
    • Source: International Mathematics Research Notices, v. 2015, (1), 2015, p. 240-287
    • Year: 2015


14. Positive Representations of Non-simply-laced Split Real Quantum Groups
    • Author(s): Ip, Ivan Chi Ho
    • Source: Journal of Algebra, v. 425, March 2015, p. 245-276
    • Year: 2015


15. Supersymmetry and the Modular Double
    • Author(s): Ip, Ivan Chi Ho; Zeitlin, Anton M
    • Source: Contemporary Mathematics, v. 623, 2014, p. 81-91
    • Year: 2014


16. Positive Representations of Split Real Quantum Groups and Future Perspectives
    • Author(s): Frenkel, I.B.; Ip, Ivan Chi Ho
    • Source: International Mathematics Research Notices, v. 2014, (8), January 2014, p. 2126-2164
    • Year: 2014


17. Q-Operator and Fusion Relations for U_q(C⁽²⁾(2))
    • Author(s): Ip, Ivan Chi Ho; Zeitlin, A.M.
    • Source: Letters in Mathematical Physics, v. 104, (8), July 2014, p. 1019-1043
    • Year: 2014


18. The Classical Limit of Representation Theory of the Quantum Plane
    • Author(s): Ip, Ivan Chi Ho
    • Source: International Journal of Mathematics, v. 24, (4), April 2013, article number 1350031
    • Year: 2013


19. Representation of the Quantum Plane, Its Quantum Double, and Harmonic Analysis on GL_q⁺(2, ℝ)
    • Author(s): Ip, Ivan Chi Ho
    • Source: Selecta Mathematica, New Series, v. 19, (4), November 2013, p. 987-1082
    • Year: 2013

  Conference paper

1. On the parabolic positive representations of split real quantum groups
   • Author(s): Ip, Ivan Chi Ho
   • Source: Proceedings of the Symposium on Representation Theory, November 2020, p. 93-105
   • Year: 2020


2. On the work of Igor Frenkel
   • Author(s): Duncan, John; Etingof, Pavel; Ip, Ivan Chi Ho; Khovanov, Mikhail; Libine, Matvei; Licata, Anthony; Savage, Alistair; Schlosser, Michael
   • Source: Contemporary Mathematics, v. 610, 2014, p. 1-21
   • Year: 2014


3. Positive Representations, Multiplier Hopf Algebra, and Continuous Canonical Basis
   • Author(s): Ip, Ivan Chi Ho
   • Year: 2013


4. Positive Representations of Split Real Quantum Groups
   • Author(s): Ip, Ivan Chi Ho
   • Source: Nankai Series in Pure, Applied Mathematics and Theoretical Physics: Symmetries and Groups in Contemporary Physics, v. 11, 2012, p. 175-180
   • Year: 2012