Dr Melissa Evelyn Tacy

PhD: Australian National University 2010

Research | Current

I work in the intersection of microlocal, semiclassical and harmonic analysis. Key problems I am interested in are

  • How do high energy solutions to PDE and pseudodifferential equations behave? What kind of concentration properties do they display? Typically these kinds of problems involved proving a growth bound for a function norm.
  • How do these concentration properties fit in with the theories and hypothesis of Quantum Chaos?
  • How can we use growth bounds for solutions to obtain mapping norm estimates for classical harmonic analysis operators (such as Bochner-Riesz means)?
  • How can we use Fourier integral opeartors to produce effective analysis/synthesis systems?
  • How do random waves behave, what can we expect at a small scale?

Selected publications and creative works (Research Outputs)

As of 29 October 2020 there will be no automatic updating of 'selected publications and creative works' from Research Outputs. Please continue to keep your Research Outputs profile up to date.
  • Han, X., & Tacy, M. (2020). Equidistribution of Random Waves on Small Balls. Communications in Mathematical Physics, 376 (3), 2351-2377. 10.1007/s00220-019-03628-9
  • Tacy, M. (2018). A note on constructing families of sharp examples for $L^{p}$ growth of eigenfunctions and quasimodes. Proceedings of the American Mathematical Society, 146 (7), 2909-2924. 10.1090/proc/14028
  • Tacy, M. (2017). The quantization of normal velocity does not concentrate on hypersurfaces. Communications in Partial Differential Equations, 42 (11), 1749-1780. 10.1080/03605302.2017.1390676
  • Han, X., & Tacy, M. (2015). Sharp norm estimates of layer potentials and operators at high frequency. Journal of Functional Analysis, 269 (9), 2890-2926. 10.1016/j.jfa.2015.06.011
  • Hassell, A., & Tacy, M. (2015). Improvement of eigenfunction estimates on manifolds of nonpositive curvature. Forum Mathematicum, 27 (3).10.1515/forum-2012-0176
  • Hassell, A., & Tacy, M. (2012). Semiclassical L p Estimates of Quasimodes on Curved Hypersurfaces. Journal of Geometric Analysis, 22 (1), 74-89. 10.1007/s12220-010-9191-7
  • Tacy, M. (2010). Semiclassical L Estimates of Quasimodes on Submanifolds. Communications in Partial Differential Equations, 35 (8), 1538-1562. 10.1080/03605301003611006

Contact details

Office hours

Tuesday 10am-11am

Thursday 4pm-5pm

Primary office location

SCIENCE CENTRE 303 - Bldg 303
Level 2, Room 229C
38 PRINCES ST
AUCKLAND CENTRAL
AUCKLAND 1010
New Zealand