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)
- (with J. Huang) "Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes", Probab. Theory Relat. Fields, 2024, arXiv:2305.04131
- (with M. Chidambaram, H. Lee, S. 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
- (with S. Matsumoto) "Moments of random quantum marginals via Weingarten calculus", Int. Math. Res. Not. IMRN., 2023, https://arxiv.org/abs/2210.11349
- (with B. Collins) "Projections of orbital measures and quantum marginal problems", Trans. Amer. Math. Soc., 376, 5601-5640, 2023, arXiv:2112.13908
- (with J. Novak) "Majorization and spherical functions", Int. Math. Res. Not. IMRN., 2021, arXiv:2006.08541
- "Box splines, tensor product multiplicities and the volume function", Algebr. Comb., 4, 435-464, 2021, arXiv:1909.12278
- "The Harish-Chandra integral: An introduction with examples", Enseign. Math., 67, 229-299, 2021, arXiv:1806.11155
- (with J. Leake, N. 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
- (with J. Raber, I. Miers, 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
- (with R. Coquereaux, J.-B. Zuber) "On Horn's problem and its volume function", Comm. Math. Phys., 376, 2409-2439, 2020, arXiv:1904.00752
- (with R. Coquereaux, J.-B. Zuber) "Revisiting Horn's problem", J. Stat. Mech.: Theory Exp, 2019, arXiv:1905.09662
- "A new proof of Harish-Chandra's integral formula", Comm. Math. Phys., 365, 239-253, 2019, arXiv:1712.03995