Dr. Kahng has been always interested in how mathematics plays a fundamental role in understanding the nature. His area of research is in Functional Analysis and Operator Algebras. Combining techniques of analysis and abstract algebra, he explores mathematical problems related to quantum physics. In classes, he strides to motivate students to gain the “big picture”, by showing various applications of mathematics underlying many different science topics. He believes that richer appreciation of mathematics occurs in this way. He has taught general introductory courses, standard calculus courses, as well as upper-division courses in analysis, algebra, geometry. In addition, he has supervised student projects on various topics, including tilings, special relativity, quantum computing, cholera epidemics, and the like.
- Supported by IMPAN for a two-month stay in Poland (Warsaw, Poland, 2019), as part of the project "New Geometry of Quantum Dynamics' supported by EU grant H2020-MSCA-RISE-2015-691246 and co-financed by Polish Government grants. 328941/PnH/2016 and W2/H2020/2016/317281.
- Fulbright U.S. Scholar (2012-2013): Conducted research with the modern analysis group at Katholieke Universiteit Leuven, Belgium, where he was appointed as a Visiting Professor.
- Research Experiences for Undergraduates (REU) grant (2008-2010), funded by the National Science Foundation (NSF): Together with Drs. Terry Bisson and Stratos Prassidis. The title of the program was "Geometry and Physics on Graphs".
- Invited speaker at PARC Winter School on Operator Theory and Operator Algebras, Korea (2011): Gave a week-long series of lectures on "Quantization, Quantum groups, and Operator Algebras", and a lecture notes was produced.
- President's Summer Research/Publication Fellowship from Canisius College (2014). In addition, was awarded Dean's Summer Research Grant multiple times.
- U.S. Department of Education National Need Fellowship (1990-1992).
A selection of Dr. Kahng's publications includes:
"A class of C*-algebraic locally compact quantum groupoids Part II. Main theory [with A. VanDaele]", Advances in Mathematics, v354 (2019), 106761 (85 pages).
"Larson-Sweedler theorem for weak multiplier Hopf algebras [with A. Van Daele]", Communications in Algebra, v46 (2018), 1--27.
"Fourier transforms on locally compact quantum groups", Journal of Operator Theory, v64 (2010), 69--87.
"Quantizations of some Poisson-Lie groups: The bicrossed product construction", Journal of Geometry & Physics, v56 (2006), 485--511.
"Non-compact quantum groups arising from Heisenberg type Lie bialgebras", Journal of Operator Theory, v44 (2000), 303--334.
"Deformation quantization of certain nonlinear Poisson structures", International Journal of Mathematics, v9 (1998), 599--621.