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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 2018-19 I also worked with Jean-Bernard Zuber as a Chateaubriand Fellow at the Laboratoire de Physique Théorique et Hautes Energies, Sorbonne University.



   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: 5601-5640. 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: 435-464. arXiv:1909.12278
  • C. McSwiggen (2021). “The Harish-Chandra integral: An introduction with examples.” Enseign. Math. 67: 229-299. arXiv:1806.11155
  • R. Coquereaux, C. McSwiggen, J.-B. Zuber (2020). “On Horn’s problem and its volume function.” Comm. Math. Phys. 376: 2409-2439. 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 Harish-Chandra’s integral formula.” Comm. Math. Phys. 365: 239–253. arXiv:1712.03995
   Algorithms, cryptography, data science:
  • M. Chidambaram, H. Lee, C. McSwiggen, S. Rezchikov (2024). "How flawed is ECE? An analysis via logit smoothing." Submitted. arXiv:2402.10046
  • J. Leake, C. McSwiggen, N. Vishnoi (2022). “Sampling matrices from Harish-Chandra-Itzykson-Zuber 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 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.
  • 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. Bar-Yam (2015). “Visualizing the 'heartbeat' of a city with tweets.” Complexity 21: 280-287. arXiv:1411.0722

Talks and presentations


  • Discrete Mathematics (MATH-UA 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
  • Monte-Carlo Simulation with Applications to Finance (APMA 1720), Brown University, Fall 2016 - Recitation leader

Other stuff

If you're looking for my non-mathematical work, there's a partial archive at my unmaintained personal website.