I'm 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 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:
 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: 435464. arXiv:1909.12278
 C. McSwiggen (2021). “The HarishChandra 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: 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 (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. 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. BarYam (2015). “Visualizing the 'heartbeat' of a city with tweets.” Complexity 21: 280287. arXiv:1411.0722
Talks and presentations
 Probability and the City Seminar, 22 October 2021.
 "Cousins and ancestors of the arithmeticgeometric inequality," CUNY Representation Theory Seminar, 15 October 2021.
 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
 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.
