Jesse Gell-Redman, Senior Lecturer at the University of Melbourne

Senior Lecturer

School of Mathematics and Statistics

University of Melbourne, VIC 3010, Australia

Peter Hall Building, Office 202

Contact

email: jgell `at' unimelb.edu.au    phone: +61383443641

About me

I am a member of the analysis subgroup in the pure math(s) research group in the University of Melbourne School of Mathematics and Statistics.

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).

Activities

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

We have a workshop at MATRIX coming up in September 2023. 

Advising

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.

Papers

In the past I have participated in discussions with members of the 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. Scattering regularity for small data solutions to the nonlinear Schrödinger equation.  With Andrew Hassell and Sean Gomes.  On arxiv.

  2. Price's law on Minkowski space in the presence of an inverse square potential.  With Dean Baskin and Jeremy Marzuola.  On arxiv.

  3. Propagation of singularities and Fredholm analysis of the time-dependent Schrödinger equation.  With Andrew Hassell and Sean Gomes.  To appear in American Journal of Mathematics.  On arxiv.

  4. Asymptotics of the radiation field for the massless Dirac-Coulomb system.  With Dean Baskin and Robert Booth.  On arxiv. To appear in Journal of Functional Analysis.

  5. Regularity of the scattering matrix for nonlinear Helmholtz Eigenfunctions.  With Jacob Shapiro and Andrew Hassell.  On arxiv. To appear in Journal of Spectral Theory.

  6. Riemann moduli spaces are quantum ergodic With Dean Baskin, Xiaolong Han.  arXiv link.  Journal of Differential Geometry. Volume 123 (2023), no. 3, 391-410

  7. The index formula for families of Dirac-type operators on pseudomanifolds. With Pierre Albin.  On arxiv.  To appear in Journal of Differential Geom.

  8. Existence and asymptotics of nonlinear Helmholtz eigenfunctions With Andrew Hassell, Jacob Shapiro, Junyong Zhang.  SIAM J. Math. Anal. 52 (2020), no. 6, 6180-6221.

  9. Spectral and Hodge theory of `Witt' incomplete cusp edge spaces. With Jan Swoboda.  arXiv link. To appear in Commentarii Mathematici Helvetici.  94 (2019), no. 4, 701-765

  10. Equidistribution of phase shifts in obstacle scattering. With Maxime Ingremeau.   arXiv link.  Comm. Partial Differential Equations. Volume 44, Issue 1,  (2019), 1–19

  11. The distribution of phase shifts for semiclassical potentials with polynomial decay. With Andrew Hassell.  IMRN. Vol 2020, no. 19.

  12. The index of Dirac operators on incomplete edge spaces. With Pierre Albin.  SIGMA 12 (2016), 089, 45 pages

  13. The Feynman propagator on perturbations of Minkowski space. With Nick Haber, and Andras Vasy.  Communications in Mathematical Physics, Volume 342, Issue 1, 2016, Pages 333–384.

  14. Harmonic maps into conic surfaces with cone angles less than 2π.  Communications in Analysis and Geometry, Volume 23, Issue 4, 2015, Pages 717–796

  15. Equidistribution of phase shifts in semiclassical potential scattering. With Andrew Hassell, and Steve Zelditch.  Journal of the London Mathematical Society, Volumn 91, Issue 1, 2015, 159–179.

  16. Approximation and equidistribution of phase shifts: spherical symmetry. With Kiril Datchev, Andrew Hassell, and Peter Humphries.  Communications in Mathematical Physics, Volume 326, Issue 3, 2014, Pages 209–236

  17. Potential scattering and the continuity of phase shifts. With Andrew Hassell.  Mathematical Research Letters, Volume 19, Issue 3, 2012, Pages 719–729.

  18. Hodge cohomology of some fibred boundary and fibred cusp metrics. With Frederic Rochon.  Mathematische Nachrichten, Volumn 288, Issue 2-3, 2015, 206–223

  19. Shrinking the period lengths of continued fractions while still capturing convergents. With Edward B. Burger, Ross Kravitz, Daniel Walton, and Nicholas Yates.  Journal of Number Theory, Volume 128, Issue 1, 2008, Pages 144–153.