P Cvitanović Turbulence in spacetime overheads (Apr 13, 2023 Working across scales in complex systems  Emory  15 min) 
If there is one idea you should take from everything presented on this webpage, it is this: stop integrating unstable, turbulent, chaotic systems forward in time. Describe instead the repertoire of admissible spatiotemporal patterns, starting with the smallest, and working your way up to larger spatiotemporal domains.  
P Cvitanović Recurrent solutions and dynamics of turbulent flows, as seen in experiments overheads (Sep 24, 2022 Georgia Tech Math Colloquium  44 min) 
In the world of moderate, everyday turbulence of fluids flowing across planes and down pipes, a quiet revolution is taking place. Today we routinely compute 'exact coherent structures', numerically precise 3D, fully nonlinear NavierStokes solutions: unstable equilibria, traveling waves, and (relative) periodic orbits. Experiments carried out at Georgia Tech (starts at min 24:15 of the video) measure 'exact coherent structures' and trace out their unstable manifolds. What emerges is a dynamical systems theory of lowReynolds turbulence as a walk among sets of weakly unstable invariant solutions.  
P Cvitanović Field theory of spatiotemporal chaos overheads (Jan 26, 2023 Georgia Tech Math Physics seminar  XX min) 
Gutzwiller semiclassics, Ruelle zeta functions, stat mech partition functions, and QFT path integrals are here developped in a common fieldtheoretic description of both (lowdimension) chaotic dynamical systems, and (infinitedimension) spatiotemporally turbulent flows, in a lattice discretized fieldtheoretic framework.  
P Cvitanović Herding cats: turbulence in spacetime (Mar 29, 2022 talk in the Newton Institute TURW04 "Wallbounded turbulence: beyond current boundaries" workshop  25 min) 
An introduction into the spatiotemporal deterministic field theory of chaos. In particular, we explain that the probability of a given spatiotemporal solution is given by the inverse of its Hill determinant.  
P Cvitanović
Hearding cats : chaotic field theory overheads (December 6, 2021 QM3 Quantum Matter meets Maths, Lisbon  1 h talk) 
Emphasizes quantum physics motivation.  
P Cvitanović
Are clouds supercomputers in the sky? overheads (March 4, 2021 Mathematics Colloquium, The Simons Center for Geometry and Physics, Stony Brook, NY  55 min talk)  
P Cvitanović
Spatiotemporal cat : a chaotic field theory overheads (December 16, 2020 Mathematical Physics Webinar, Rutgers University  55 min talk)  
P Cvitanović
Herding cats : a chaotic field theory overheads (September 25, 2020 ITS Symposium on Chaos and Quantum Field Theory  1 hour talk)  abstract  video (1 hour 10 min)  
P Cvitanović and H Liang
Herding cats : a chaotic field theory overheads (July 2020)  video (similar to 2020 APS below, but 1h long)  
P Cvitanović, H Liang and M N Gudorf
Is space time? a spatiotemporal tiling of turbulence overheads (March 2, 2020 APS March Meeting  30 min talk) 
Revolution will not be twitterized!. 

P Cvitanović and M Gudorf A spatiotemporal theory of turbulence  computational challenges overheads (October 12, 2020 Intern. Conf. Computer Simulation in Physics and beyond CSP2020, Moscow  40 min plenary talk) 

Matthew N. Gudorf
Spatiotemporal tiling of the KuramotoSivashinsky system thesis (November 20, 2020  1 hour talk) Georgia Tech thesis repository link  
P Cvitanović: Dynamical systems are a fraud! ChaosBook.org/course1 (5:40 min manifesto Jan 11, 2022)  Act locally, think globally, tighten the rubber band: elaborated a bit in the next two videos.  
P Cvitanović: What do we talk about when we talk about chaos I (9:41 min, July 29, 2020)  When we talk, we talk about evolving in time, derive the forwardintime Jacobian.  
P Cvitanović: What do we talk about when we talk about chaos II (8:40 min July 30, 2020)  When we walk the walk, we determine the global orbit and its global stability, derive its orbit Jacobian.  
Spatiotemporal blog
(Nov 6, 2022)
OrbitHunter (Oct 01, 2021) 
Working notes very rough, read at your own risk, but with lots of literature pointers on how to recast finding invariant solutions of the 1D KuramotoSivashinsky PDE into the problem of finding spatiotemporal fixed point solutions. We have give up on finding compact solutions by forward integration in time  instead, we develop variational methods to multiplyperiodic solutions in spacetime. In particular, it would be very nice if someone extends OrbitHunter to a general spatiotemporal NavierStokes solver that runs on a higly parallelized machines. 

Predrag Cvitanović
Chaotic Field Theory: a sketch, Physica A 288 , 61 (2000) [ arXiv:nlin.CD/0001034  DOI  NSF review panel critique ] 