I'm Colin McSwiggen, a Courant Instructor and NSF Postdoctoral Fellow at New York University's Courant Institute of Mathematical Sciences. My research investigates how randomness and symmetry interact to produce numerous phenomena in mathematics and in the world.
Specifically, I use tools from both algebra and analysis to study probability measures that are invariant under a Lie group action, along with related special functions. Since these are ubiquitous objects, in practice I work on problems connected to several areas, including random matrix theory, combinatorial representation theory, quantum information, and harmonic analysis. I also collaborate with physicists and computer scientists on applications in their respective fields.
I completed my PhD in 2020 at Brown University, where my advisor was Govind Menon. In 201819 I also worked with JeanBernard Zuber as a Chateaubriand Fellow at the Laboratoire de Physique Théorique et Hautes Energies, Sorbonne University.
Research
Pure math and mathematical physics:
 J. Huang, C. McSwiggen (2023). "Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes." Submitted. arXiv:2305.04131
 S. Matsumoto, C. McSwiggen (2023). "Moments of random quantum marginals via Weingarten calculus." Int. Math. Res. Not. IMRN.: rnad105. arXiv:2210.11349
 B. Collins, C. McSwiggen (2023). "Projections of orbital measures and quantum marginal problems." Trans. Amer. Math. Soc. 376: 56015640. arXiv:2112.13908
 C. McSwiggen, J. Novak (2021). “Majorization and spherical functions.” Int. Math. Res. Not. IMRN.: rnaa390. arXiv:2006.08541
 C. McSwiggen (2021). “Box splines, tensor product multiplicities and the volume function.” Algebr. Comb. 4: 435464. arXiv:1909.12278
 C. McSwiggen (2021). “The HarishChandra integral: An introduction with examples.” Enseign. Math. 67: 229299. arXiv:1806.11155
 R. Coquereaux, C. McSwiggen, J.B. Zuber (2020). “On Horn’s problem and its volume function.” Comm. Math. Phys. 376: 24092439. arXiv:1904.00752
 R. Coquereaux, C. McSwiggen, J.B. Zuber (2019). “Revisiting Horn’s problem.” J. Stat. Mech.: Theory Exp. 2019: 094018. arXiv:1905.09662
 C. McSwiggen (2019). “A new proof of HarishChandra’s integral formula.” Comm. Math. Phys. 365: 239–253. arXiv:1712.03995
Algorithms, cryptography, data science:
 J. Leake, C. McSwiggen, N. Vishnoi (2022). “Sampling matrices from HarishChandraItzyksonZuber densities with applications to quantum inference and differential privacy.” Submitted. arXiv:2011.05417
(Expanded journal version of STOC paper.)
 J. Leake, C. McSwiggen, N. Vishnoi (2021). “Sampling matrices from HarishChandraItzyksonZuber densities with applications to quantum inference and differential privacy.” STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing: 13841397.
 J. Raber, I. Miers, C. McSwiggen, Y. Zhu, D. Lai, M. Green, S. He, A.S. Raja (2021). “A cryptographic framework for lotteries in medical triage: secure and transparent randomized allocation of scarce healthcare resources.” AMIA 2021 Virtual Clinical Informatics Conference.
 U. França, H. Sayama, C. McSwiggen, R. Daneshvar, Y. BarYam (2015). “Visualizing the 'heartbeat' of a city with tweets.” Complexity 21: 280287. arXiv:1411.0722
Talks and presentations
 Randomness and LieTheoretic Structures, University of Virginia, 45 March 2024.
 Probability Seminar, University of Cincinnati, 21 November 2023.
 Analysis Seminar, Yale University, 16 November 2023.
 BielefeldMelbourne Random Matrix Theory Seminar, 4 October 2023.
 "Dunkl theory at Large N," Stochastic Processes and their Applications (SPA2023), Invited Session on Integrable Probability, University of Lisbon, 27 July 2023.
 "Dunkl theory at Large N," Random Matrices and Applications, Research Institute for Mathematical Sciences, Kyoto University, 6 June 2023.
 Colloquium lecture, Institute of Mathematics, Academia Sinica, Taipei, 2 February 2023.
 "Sampling from unitary orbits, and an application to differential privacy," Applied Math Seminar, Brandeis University, 12 December 2022.
 Analysis and Probability Research Group Seminar, Indian Institute of Science, 30 March 2022.
 "Sampling matrices from HarishChandraItzyksonZuber distributions," Simons Institute Workshop on Optimization Under Symmetry, UC Berkeley, 30 November 2021. (video)
 "Random matrix ensembles constructed from projections of orbital measures," Probability and the City Seminar, 22 October 2021. (video)
 "Cousins and ancestors of the arithmeticgeometric inequality," CUNY Representation Theory Seminar, 15 October 2021. (video)
 TokyoKyoto Online Operator Algebras Seminar, 7 January 2021.
 "Horn's problem, polytope volumes and tensor product decompositions," Operator Algebras Seminar, University of Tokyo, 29 January 2020.
 Kyoto Operator Algebra Seminar, Kyoto University, 24 January 2020.
 Combinatorics Seminar, Brown University, 20 November 2019.
 "From multiplicities to random matrices and back again," AMS Fall Western Sectional Meeting, Special Session on Random Matrices and Related Structures, UC Riverside, 910 November 2019.
 "Multiplicities from volumes," Integrability, Combinatorics and Representations, Giens, France, 26 September 2019.
 "LargeN asymptotics of HarishChandra integrals," Randomness and Symmetry, University College Dublin, 1822 June 2018.
Teaching
 Discrete Mathematics (MATHUA 120), New York Univeristy, Fall 2022  Instructor of record
 Introduction to Stochastic Differential Equations (APMA 1930U), Brown University, Fall 2019  Recitation leader
 Operations Research: Probabilistic Methods (APMA 1200), Brown University, Spring 2017  Recitation leader
 MonteCarlo Simulation with Applications to Finance (APMA 1720), Brown University, Fall 2016  Recitation leader
Other stuff
If you're looking for my nonmathematical work, there's a partial archive at my unmaintained personal website.
