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I'm

Colin McSwiggen

, a postdoctoral researcher in the Department of Mathematical Sciences at the University of Tokyo. 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.


email: contact@cosmc.net



Research



   Pure math and mathematical physics:
  • C. McSwiggen, J. Novak (2021). “Majorization and spherical functions.” To appear in Int. Math. Res. Not. IMRN. arXiv:2006.08541
  • C. McSwiggen (2021). “Box splines, tensor product multiplicities and the volume function.” To appear in Algebr. Comb. arXiv:1909.12278
  • 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
  • C. McSwiggen (2018). “The Harish-Chandra integral.” Submitted. arXiv:1806.11155
   Algorithms, cryptography, data science:
  • J. Leake, C. McSwiggen, N. Vishnoi (2020). “A polynomial-time algorithm and applications for matrix sampling from Harish-Chandra-Itzykson-Zuber densities.” Submitted. arXiv:2011.05417
  • I. Miers, C. McSwiggen, Y. Zhu, D. Lai, M. Green, S. He, A.S. Raja (2020). “A cryptographic framework for lotteries in medical triage: secure and transparent randomized allocation of scarce healthcare resources.” Submitted.
  • 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


  • 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.