Alexei A. Mailybaev


Laboratory of Fluid Dynamics

Instituto Nacional de Matemática Pura e Aplicada - IMPA

Estrada Dona Castorina 110, Rio de Janeiro 22460-320 Brazil



Tel.: +55 21 2529 5070


CV: in English [PDF] , in Portuguese [CNPq Lattes]

Profile in [Google Scholar]


Brazilian Chapter of InterPore (The International Society for Porous Media): co-founder (2014) and first chair (2014-9).

The latest:

Sabine Hossenfelder's YouTube video about our recent paper in Physical Review Letters 132, 104002 (2024).

1-day workshop: Mathematical challenges in turbulence. Tuesday, February 27. Auditorium 1 - IMPA


Course "Hidden symmetries in fluid dynamics" (with Simon Thalabard, U. Nice)

Wed & Fri, 10/1-2/2 at 15:00-17:00 in room 232.

VIDEOS on IMPA's YouTube Channel:

Lecture 1: Navier-Stokes (NS) and Euler equations. Symmetries. Conservation of energy.

Lecture 2: NS turbulence, Gaussian HIT, Gaussian vs. NS, viscous effects.

Lecture 3: Scaling  anomaly, Random-h model, Multifractal theory.

Lecture 4: Solvable intermittent model of turbulence.

Lecture 5: Hidden scaling symmetry in shell models. Anomalous scaling laws.

Lecture 6: Kolmogorov multipliers. Rescaled NS equations.

Lecture 7: Hidden symmetries in NS turbulence.

Lecture 8: Group theory approach to hidden scaling symmetries.

Lecture 9: Group theory approach to quasi-Lagrangian formalism. Perspectives.

Notes: Simon (lecture_1, lecture_2, lecture_3, lecture_6_7) & Alexei (lecture_4_5_6, lecture_8_9)

Mini-course "Turbulence predictability and spontaneous stochasticity"

Summer school : 100 Years of Turbulent Cascades, Nice-Porquerolles, June, 2023.

VIDEO with the password R(two)(three) 

Lecture "Spontaneous stochasticity", October 18, 2022:  VIDEO

Conference IMPA 70 years, Rio de Janeiro

Lecture "Spontaneous stochasticity and RG in discrete multi-scale dynamics" July 19, 2022: VIDEO

JHU/Lyon Turbulence Seminar

Lecture "Spontaneous stochasticity and renormalization group in discrete multi-scale dynamics" June 13, 2022: VIDEO

Lecture "Hidden scale invariance in turbulence" June 10, 2022: VIDEO

The Simons Center for Geometry and Physics, Stony Brook.

Course Linear Algebra and Applications (March-June 2022): Thursday at 10:30, Friday at 9:30. VIDEO

Course Topics in Mathematics of Turbulence  (January-February 2022). VIDEO

IMPA Summer School course (January-February 2021):

Introduction to the Theory of Oscillations and Waves

January-February, Wednesday/Thursday/Friday, 10:00-12:00. 

Online: feel free to ask me for the link by email. For more information click here.

Lecture "Spontaneously stochastic solutions". Online conference TURB1D 2020.

Tuesday 24th November, 14h00 - 15h00 (central EU time). Presentation.

Lecture "Hidden spatiotemporal symmetries and intermittency" at the Meeting in Turbulence: Problems at the Interface of Mathematics and Physics, ICTS, Bangalore, 1-12 November 2021. SLIDES and  VIDEO,

Lectures on "Hidden spatiotemporal symmetries and intermittency in turbulence". JHU/Lyon meeting (in Zoom): 

  • Part 1: Overview and construction with temporal scalings. November 4 at 9:30 am Eastern US time.
  • Part 2: Intermittency. November 11 at 9:30 am Eastern US time.
  • Part 3: Galilean transformations, final normalized system, application to NS. November 18 at 9:00 am Eastern US time. Presentation

Lecture at the Computational & Applied. Math. seminar: "Numerical simulation of immiscible two-phase Rayleigh-Taylor turbulence". Friday, September 18 at 8.a.m. Bogotá time. Zoom link:

IMPA's press: Pesquisadores do IMPA abordam precisão das modelagensAbout our paper "From the butterfly effect to spontaneous stochasticity in singular shear flows".

Course "Álgebra Linear e Aplicações", IMPA, Rio de Janeiro

See more details about the course HERE

Lecture "From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows". Rio Summer School on PDEs, Centro de Ciências Matemáticas e da Natureza UFRJ, Rio de Janeiro. March 13, 14:40-15:20.

Lecture "Explosive ripple instability due to incipient wave breaking" at the seminar of academician Vladimir E. Zakharov "Nonlinear waves" on February 26th at 14:30. Skoltech (Moscow, Russia), Nobelya 1, room 249. (slides)

Lecture "Inteligência artificial e desafios computacionais em Dinâmica de Fluidos", 1o Workshop Matemática e Indústria, IMPA - Rio de Janeiro, February 13-14, 2020. (video)

IMPA Summer School advanced course (January-February 2020)

Thermal and Statistical Aspects of Fluid Dynamics (together with Simon Thalabard)

Tue, Wed, Fri 15:00-17:00, room 224, starting on January 7.

Description, LECTURE NOTES

IMPA's press release on our paper "Explosive ripple instability due to incipient wave breaking"

Lecture "Calculus and flows on logarithmic lattices" at the Colloquium of the Mathematical Department of PUC, Rio de Janeiro, November 12, 2019.

Lecture "Control of wave pulses with exceptional points" at the One day workshop on counterintuitive phenomena controlled by exceptional points (EPs), Technion, Haifa, Israel (2d floor at the Theoretical Chemistry), 28 October 2019.

Lecture “Chaotic blow-up scenarios in models and DNS” at the Day Workshop “Singularity and Irreversibility” at CEA Saclay, France, October 16. ProgramSlides

Ph.D. student of our Fluid Dynamics Lab Ciro Sobrinho Campolina Martins is receiving the Premium for the best M.Sc. dissertation from the Brazilian Society of Applied and Computational Mathematics (SBMAC)

IMPA's press release 

Conference on "Universal features of hydrodynamical, optical and wave turbulence": Nice, France, September 9-12, 2019. Program

17th European Turbulence Conference: Torino, Italy,  September 3-6, 2019. Program, Slides

3d BR InterPore Conference on Porous Media: LNCC, Petropolis, August 5-8, 2019. ProgramOpenningBR-Chapter, Slides

Parametric Resonance (Lecture notes) (Video): São Paulo School of Advanced Sciences on NONLINEAR DYNAMICS, July 29 - August 9, 2019.

Thematic Session "Mathematical and Computational Aspects of Fluid Dynamics" at the Brazilian Mathematical Colloquium: IMPA, Monday and Tuesday, July 29-30 at 9:00-13:00. Program

Our paper on a cover of the Journal of Fluid Mechanics:

Talk "Spontaneously stochastic solutions developing from singularities" (Weizmann Institute of Science, Israel, December 17, 11:00). SRitp Workshop on Fluid flows, from Graphene to planet atmospheres.

Solid State Institute Seminar "Exceptional points and stopping of light" (Solid State Auditorium, Technion, Israel. December 12, 12:30).

Mathematical Physics Seminar "Exceptional points and stopping of light" (Imperial College London, UK. November 28, 14:00). SLIDES

Mathematical Physics / Fluids seminar "Spontaneously stochastic solutions from singularities in differential equations" (University of Bristol, UK. November 26, 14:00).

Seminar "Explosive ripple instability due to incipient wave breaking" (Università degli Studi di Roma Tor Vergata, Italy. November 12, 14:30, Sala Fisica della Materia). SLIDES

Seminar "Chaotic Blowup in the 3D Incompressible Euler Equations on a Logarithmic Lattice" (IRAMIS: Saclay Institute of Matter and Radiation, France. November 7, 11:30).

Talk "Chaotic blowup in the 3D incompressible Euler equations on a logarithmic lattice" at GDR Phénoménologie de la Turbulence (Université de Nice, France. October 16).

Mini-course: "Spontaneous Stochasticity" (Observatoire de la Côte d’Azur, Nice, France. October 5 and 11, 10:00, salle Michel Hénon). 

Talk "Explosive ripple instability due to incipient wave breaking " at the Workshop on Mathematical and Computational Problems of Incompressible Fluid Dynamics (IMPA, Rio de Janeiro, August 11, 11:40, room 228).

Seminário q.t.p. Turbulência hidrodinâmica: no cruzamento entre Matemática, Física e Engenharia. Matemática PUC-Rio, 12 de junho, 17:30, sala 856L. 

Credit: pixabay 

Our paper on stopping light featured by Newsweek, The IndependentDaily MailInternational Business Times, Europa In Portuguese: IMPA's press release, Destaque em SBF, Revista Pesquisa Fapesp

Talk "Solutions of differential equations from a non-Lipschitz singularity" at the Seminar on Dynamical Systems, Jan. 24, 2018.

Interview in the book: "A vista do Rio" by Luiza Mussnich, Gustavo da Rocha Lima, Alex Ward (Rio de Janeiro: ID Cultural, 2017).

Talk "Solutions after blowup in ODEs and PDEs: spontaneous stochasticity" at the seminar on Analysis of Fluids and Related Topics (Math. Dept., Princeton University), Oct. 19, 2017.

Video: Talk "Inviscid limit for the Rayleigh-Taylor instability as a spontaneously stochastic dynamics" at the Workshop on Geometrical and Statistical Fluid Dynamics in the Simons Center for Geometry and Physics, Stony Brook, Oct. 13, 2017.

Video: Talk "Non-local 1D conservation laws: when the shock wave is unstable" at the Workshop on Conservation Laws and Applications, celebrating the 70th birthday of Dan Marchesin 

 InterPore Rosette

 Interview for Galileu (March 2017), in Portuguese.

Video: Lecture "Spontaneously stochastic solutions from singular initial data" at IMPA-Bath Workshop.

IMPA-Bath Workshop in Mathematics. January 23 - 27, 2017, IMPA, Rio de Janeiro.

Videos: Workshop on Turbulent Dissipation, Mixing and Predictability. January 9 - 13, 2017, IPAM, Los Angeles.

Videos: 2nd IMPA-InterPore Conference on Porous Media. October 16-19, 2016, IMPA, Rio de Janeiro.

Dieter Heiss, Mathematical physics: Circling exceptional points (News & Views of Nature Physics about our paper)