Prof Todd Oliynyk

Research Overview

My main research interests are in partial differential equations, analysis, mathematical physics, and geometry. Specific topics where I have made contributions or on which I am currently working are:

(I.) Hyperbolic PDEs: singular limits, Fuchsian PDEs, system of wave equations, free-boundary problems, global existence problems.

(II.) General relativity: Newtonian limit, post-Newtonian expansions, Einstein-Yang-Mills, gravitating perfect fluids and elastic bodies, global existence and future stability problems.

(III.) Geometric flows: Ricci flow, renormalization group flow.

Selected Publications

[1] Beyer, Florian, Oliynyk, Todd A ; Olvera-Santamaria, J. Arturo. "The Fuchsian approach to global existence for hyperbolic equations". In: Communications in Partial Differential Equations. 2020 (accepted). [preprint: \https://arxiv.org/abs/1907.04071, arXiv:1907.04071]

[2] Liu, Chao ; Oliynyk, Todd. "Cosmological Newtonian Limits on Large Spacetime Scales". In: Communications in Mathematical Physics. 2018 ; Vol. 364, No. 3. pp. 1195-1304. https://doi.org/10.1007/s00220-018-3214-9

[3] Oliynyk, Todd A. "A priori estimates for relativistic liquid bodies". In: Bulletin des Sciences Mathematiques. 2017 ; Vol. 141, No. 3. pp. 105-222. https://doi.org/10.1016/j.bulsci.2017.02.001

[4] Oliynyk, Todd A. "Future stability of the FLRW fluid solutions in the presence of a positive cosmological constant". In: Communications in Mathematical Physics. 2016 ; Vol. 346, No. 1. pp. 293-312. https://doi.org/10.1007/s00220-015-2551-1

[5] Andersson, Lars ; Oliynyk, Todd A ; Schmidt, Bernd G. "Dynamical compact elastic bodies in general relativity". In: Archive for Rational Mechanics and Analysis. 2016 ; Vol. 220, No. 2. pp. 849-887. https://doi.org/10.1007/s00205-015-0943-1