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I'm

Colin McSwiggen

, a mathematician on the faculty of the Institute of Mathematics at Academia Sinica, the national academy of Taiwan. 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.


email: contact@cosmc.net



Research



   Pure math and mathematical physics:
  • J. Huang, C. McSwiggen (2024). "Asymptotics of generalized Bessel functions and weight multiplicities via large deviations of radial Dunkl processes." Probab. Theory Relat. Fields. 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." ICML 2024: Proceedings of the 41st International Conference on Machine Learning, PMLR 235:8417-8435. 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




Teaching


  • 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.