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Colin McSwiggen

, a Courant Instructor and NSF Postdoctoral Fellow at New York University's Courant Institute of Mathematical Sciences. My current research focuses on the analytic and combinatorial study of orbital matrix integrals. In practice this means that 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:
  • B. Collins, C. McSwiggen (2021). "Projections of orbital measures and quantum marginal problems." In preparation.
  • 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.” To appear in Enseign. Math. 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:
  • 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. arXiv:2011.05417
  • 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


  • 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.