Timothy Candy

I am a senior lecturer in pure mathematics in the Department of Mathematics and Statistics at the University of Otago.

I arrived in Otago in 2018, after having spent time as a postdoc at the University of Bielefeld, Johns Hopkins University, and Imperial College London.

A full list of my preprints on the arXiv can be found here.

From 2019 - 2024 my research has been supported by the Marsden fast start grant 'Global Behaviour of Nonlinear Dispersive Partial Differential Equations'.

In December 2024 I organised the workshop Problems and progress in dispersive PDE that took place in Dunedin, New Zealand.

As part of joint meeting of the AMS, AustMS, and NZMS, I also (together with my coorganisors, Yu Deng, Bobby Wilson, and Xueying Yu) organised the special session Deterministic and robabilistic aspects of dispersive partial differential equations.

Contact Details

tcandy [at] maths.otago.ac.nz

Research

My research lies in the general areas of partial differential equations and harmonic analysis. I am particularly interested in understanding the global dynamics of solutions to nonlinear dispersive partial differential equations (typically nonlinear models arising in mathematical physics such as the Dirac equation, Wave maps equations, and the Maxwell-Klein-Gordon equation among others).

A key goal is to prove that for large times solutions to nonlinear problems can decouple into a linear or dispersive term, and terms exhibiting nonlinear effects such as focusing/blow-up or soliton like behavior.

I am also interested in restriction estimates, and in particular, on bilinear and multilinear restriction estimates. These estimates are closely related to estimates for linear dispersive equations (known as Strichartz estimates) and are a key tool in the study of nonlinear dispersive equations.

Recent publications (all preprints can be found on the arXiv):

T. Candy and S. Herr, The massless and the non-relativistic limit for the cubic Dirac equation [preprint]
T. Candy, Concentration compactness for the energy critical Zakharov system. Discrete & Continuous Dynamical Systems (2024). Advance online publication. doi: 10.3934/dcds.2023150. [preprint]
T. Candy, A note on bilinear wave-Schrödinger interactions, In: Wood D.R., de Gier J., Praeger C.E., Tao T. (eds) 2019-20 MATRIX Annals. MATRIX Book Series, vol 4. Springer, Cham. 537-549. [preprint]
T. Candy, S. Herr, and K. Nakanishi, The Zakharov system in dimension d>=4, Journal of the European Mathematical Society (2023), 25, 3177-3228. [preprint]
T. Candy, S. Herr, and K. Nakanishi, Global wellposedness for the energy-critical Zakharov system below the ground state, Advances in Mathematics 384 (2021).[preprint]
T. Candy, Multi-scale bilinear restriction estimates for general phases, Math. Ann. 375 (2019), no. 1, 777-843 . [preprint]
T. Candy, C. Kauffman, and H. Lindblad, Asymptotic behavior of the Maxwell-Klein-Gordon system, Commun. Math. Phys. 367 (2019), no. 2, 683-716 [34 pages]. [preprint]
T. Candy and S. Herr, On the division problem for the wave maps equation, Annals of PDE 4 (2018), no. 2, 17. [preprint]
T. Candy and S. Herr, On the Majorana condition for nonlinear Dirac systems, Annales de l’Instituté Henri Poincaré C, Analyse non linéaire 35 (2018), no. 6, 1707–1717. [preprint]
T. Candy and H. Lindblad, Long range scattering for the cubic Dirac equation on R^{1+1}, Differential Integral Equations 31 (2018), no. 7/8, 507–518 . [preprint]
T. Candy and S. Herr, Transference of bilinear restriction estimates to quadratic variation norms and the Dirac-Klein-Gordon system, Anal. PDE 11 (2018), no. 5, 1171–1240. [preprint]
T. Candy and S. Herr, Conditional large initial data scattering results for the Dirac-Klein-Gordon system, Forum of Mathematics, Sigma 6 (2018), e9. [preprint]

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