My work is in microlocal analysis and differential geometry. My research is partly supported by the Australian Research Council through Discovery Project grants DP180100589 (completed) with co-chief investigator Andrew Hassell and DP210103242 with partner investigators Pierre Albin (UIUC) and Paolo Piazza (Sapienza).

The analysis group runs a seminar, which you can find further information about here.

People interested in joining the University of Melbourne analysis group can find, among other things, information about the MSc (masters of science) analysis subjects here.

In the past I have participated in discussions with members of the (disbanded) UoM deep learning group, and joined (modestly) in the writing of this paper with lead authors Daniel Murfet and Susan Wei.

Here is a link to the arXiv search that produces all of my publicly available papers, which I list here:

  1. Baskin, D., Doll, M., & Gell-Redman, J. (2024). The Klein-Gordon equation on asymptotically Minkowski spacetimes: causal propagators.
  2. Gell-Redman, J., Gomes, S., & Hassell, A. (2023). Scattering regularity for small data solutions of the nonlinear Schrödinger equation.
  3. Baskin, D., Gell-Redman, J., & Marzuola, J. (2022). Price’s law on Minkowski space in the presence of an inverse square potential.
  4. Gell-Redman, J., Gomes, S., & Hassell, A. (2022). Propagation of singularities and Fredholm analysis of the time-dependent Schrödinger equation.
  5. Baskin, D., Booth, R., & Gell-Redman, J. (2021). Asymptotics of the radiation field for the massless Dirac-Coulomb system.
  6. Gell-Redman, J., Hassell, A., & Shapiro, J. (2022). Regularity of the Scattering Matrix for Nonlinear Helmholtz Eigenfunctions. J. Spectr. Theory.
  7. Baskin, D., Gell-Redman, J., & Han, X. (2021). Riemann moduli spaces are quantum ergodic. In J. Differential Geom.
  8. Albin, P., & Gell-Redman, J. (2021). The index formula for families of Dirac type operators on pseudomanifolds. In J. Differential Geom.*
  9. Gell-Redman, J., Hassell, A., Shapiro, J., & Zhang, J. (2020). Existence and asymptotics of nonlinear Helmholtz eigenfunctions. SIAM J. Math. Anal., 52(6), 6180–6221. https://doi.org/10.1137/19M1307238
  10. Gell-Redman, J., & Swoboda, J. (2019). Spectral and Hodge theory of “Witt” incomplete cusp edge spaces. Comment. Math. Helv., 94(4), 701–765. https://doi.org/10.4171/cmh/472
  11. Gell-Redman, J., & Ingremeau, M. (2019). Equidistribution of phase shifts in obstacle scattering. Comm. Partial Differential Equations, 44(1), 1–19. https://doi.org/10.1080/03605302.2018.1499778
  12. Gell-Redman, J., & Hassell, A. (2020). The distribution of phase shifts for semiclassical potentials with polynomial decay. Int. Math. Res. Not. IMRN, 19, 6294–6346. https://doi.org/10.1093/imrn/rny180
  13. Albin, P., & Gell-Redman, J. (2016). The index of Dirac operators on incomplete edge spaces. SIGMA Symmetry Integrability Geom. Methods Appl., 12, Paper No. 089, 45. https://doi.org/10.3842/sigma.2016.089
  14. Gell-Redman, J., Haber, N., & Vasy, A. (2016). The Feynman propagator on perturbations of Minkowski space. Comm. Math. Phys., 342(1), 333–384. https://doi.org/10.1007/s00220-015-2520-8
  15. Gell-Redman, J. (2015). Harmonic maps of conic surfaces with cone angles less than 2\pi. Comm. Anal. Geom., 23(4), 717–796. https://doi.org/10.4310/CAG.2015.v23.n4.a2
  16. Gell-Redman, J., Hassell, A., & Zelditch, S. (2015). Equidistribution of phase shifts in semiclassical potential scattering. J. Lond. Math. Soc. (2), 91(1), 159–179. https://doi.org/10.1112/jlms/jdu068
  17. Datchev, K., Gell-Redman, J., Hassell, A., & Humphries, P. (2014). Approx imation and equidistribution of phase shifts: spherical symmetry. Comm. Math. Phys., 326(1), 209–236. https://doi.org/10.1007/s00220-013-1841-8
  18. Gell-Redman, J., & Hassell, A. (2012). Potential scattering and the continuity of phase-shifts. Math. Res. Lett., 19(3), 719–729. https://doi.org/10.4310/MRL.2012.v19.n3.a15
  19. Gell-Redman, J., & Rochon, F. (2015). Hodge cohomology of some foliated boundary and foliated cusp metrics. Math. Nachr., 288(2-3), 206–223. https://doi.org/10.1002/mana.201300076
  20. Burger, E. B., Gell-Redman, J., Kravitz, R., Walton, D., & Yates, N. (2008). Shrinking the period lengths of continued fractions while still capturing convergents. J. Number Theory, 128(1), 144–153. https://doi.org/10.1016/j.jnt.2007.03.001