McSwiggen, Colin
Assistant Research Fellow
Research Fields: probability, special functions, random matrices, algebraic combinatorics, mathematical physics, machine learning theory
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 invariant probability measures and related special functions, often with a focus on high-dimensional asymptotic phenomena. 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.
Other recent work includes projects on sampling algorithms, model calibration in machine learning, and AI tools for mathematicians.
- Ph.D., Applied Mathematics, Brown University, 2020
- M.A. + M.Sc., Industrial Design Engineering, RCA/Imperial College London, 2013
- S.B., Physics, MIT, 2011
- S.B., Mathematics, MIT, 2011
- Courant Instructor & NSF Postdoctoral Fellow, New York University, 2021–2024 (Mentor: Sylvia Serfaty)
- Postdoctoral Researcher, University of Tokyo, 2020–2021 (Mentor: Yasuyuki Kawahigashi)
- 2021, NSF Mathematical Sciences Postdoctoral Research Fellowship (Courant Institute for Mathematical Sciences, New York University)
- 2020, Dunmu Ji Award, Brown University Division of Applied Mathematics (Awarded “in recognition of a particularly original and independent thesis.”)
- 2018-2019, Chateaubriand Fellowship of the Embassy of France in the United States (Laboratoire de Physique Théorique et Hautes Énergies, Sorbonne University)
- C. McSwiggen, C. Cuenca, "The rectangular finite free heat flow", (Under review), 2026
- Colin McSwiggen, Siddhartha Sahi, "Majorization inequalities from logarithmic convexity", (Under review), 2026, arXiv:2605.12680
- Owen D. Biesel, Colin McSwiggen, Ted Theodosopoulos, Michael G. Titelbaum, "Topological obstructions to shared priors", (Under review), 2025, arXiv:2512.09124
- Samuel G. G. Johnston, Colin McSwiggen, "On the limiting Horn inequalities", (Under review), 2025, arXiv:2410.08907
- Jonathan Leake, Colin McSwiggen, Nisheeth K. Vishnoi, "Sampling matrices from Harish-Chandra-Itzykson-Zuber densities with applications to quantum inference and differential privacy", Random Structures and Algorithms, 67 (2), 2025, Link
- Jiaoyang Huang, Colin McSwiggen, "Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes", Probab. Theory Relat. Fields, 2024, arXiv:2305.04131
- Muthu Chidambaram, Holden Lee, Colin McSwiggen, Semon Rezchikov, "How flawed is ECE? An analysis via logit smoothing", ICML 2024: Proceedings of the 41st International Conference on Machine Learning, 235, 8417-8435, 2024, arXiv:2402.10046
- Sho Matsumoto, Colin McSwiggen, "Moments of random quantum marginals via Weingarten calculus", Int. Math. Res. Not. IMRN., 2023, arXiv:2210.11349
- Benoît Collins, Colin McSwiggen, "Projections of orbital measures and quantum marginal problems", Trans. Amer. Math. Soc., 376, 5601-5640, 2023, arXiv:2112.13908
- Colin McSwiggen, Jonathan Novak, "Majorization and spherical functions", Int. Math. Res. Not. IMRN., 2021, arXiv:2006.08541
- Colin McSwiggen, "Box splines, tensor product multiplicities and the volume function", Algebr. Comb., 4, 435-464, 2021, arXiv:1909.12278
- Colin McSwiggen, "The Harish-Chandra integral: An introduction with examples", Enseign. Math., 67, 229-299, 2021, arXiv:1806.11155
- Jonathan Leake, Colin S. McSwiggen, Nisheeth K. Vishnoi, "Sampling matrices from Harish-Chandra–Itzykson–Zuber densities with applications to quantum inference and differential privacy", STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, 1384-1397, 2021, arXiv:2011.05417
- J. Raber, I. Miers, C. McSwiggen, Y. Zhu, D. Lai, M. Green, S. He, A.S. Raja, "A cryptographic framework for lotteries in medical triage: secure and transparent randomized allocation of scarce healthcare resources", AMIA 2021 Virtual Clinical Informatics Conference, 2021
- Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber, "On Horn's problem and its volume function", Comm. Math. Phys., 376, 2409-2439, 2020, arXiv:1904.00752
- Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber, "Revisiting Horn's problem", J. Stat. Mech.: Theory Exp, 2019, arXiv:1905.09662
- Colin McSwiggen, "A new proof of Harish-Chandra's integral formula", Comm. Math. Phys., 365, 239-253, 2019, arXiv:1712.03995