Lenya Ryzhik

How to reach me

• Paper mail:
  Department of Mathematics
  Stanford University
  Stanford CA 94305
  USA
  
  
• Office: 382U
  
• E-mail: ryzhik@math.stanford.edu
  
• Phone: (650) 721-2113 (Office)
  
• Fax: (650)-725-4066
  

Summer School at Stanford, August 5-18, 2013

Teaching

• Lecture notes for Math 256 B, Fluids part, Spring 2024
• Lecture notes for Math 256 B, SPDE part, Spring 2024
• Lecture notes from Lausanne, August 2023
• Winter 2023:
  Stanford Winter 2023 Topics in PDE lecture notes These notes will be continuously updatd back and forth.
• Fall 2021:
  Stanford Fall 2021 BBM and PDE mini-course lecture notes These notes will be continuously updatd back and forth.
• Winter 2021:
  Lecture notes for the topics in PDE class
• Math 63 CM, Winter 2020
• Stanford Spring 2020 PDE mini-course lecture notes
• Technion summer school lecture notes
• Wien lecture notes on waves in random media
• Toulousain KPP lecture notes
• Santa Barbara lecture notes
• Lecture Notes on Complex Analysis - translation of several chapters from "Introduction to Complex Analysis" by B. Shabat
  
• Winter 2019:
  Lecture notes for the fluids PDE class
• Winter 2018:
  Lecture notes for a reading course
  
• Spring 2017:
  Lecture Notes for Topics in PDE
  
• Spring 2016:
  Lecture notes for the Introduction to SPDEs
  
• Fall 2015:
  Lecture Notes for Topics in PDES, Math 272 in Fall 2015
• Winter 2014:
  Lecture Notes for Fluid PDEs Math 256B
  Lecture Notes for Topics in PDEs
  
• Fall 2011:
  Technion Lecture Notes.
  
• Winter 2003:
  (Applied Analysis Lecture Notes).
  

  Stanford Applied Math seminar

  Communications in Mathematical Sciences

  Nonlinearity (the journal, that is)

  Talks from the conference at BIRS Centre in Banff in March 2010

  Curriculum Vitae

  Click here to see a more or less up to date vita. (pdf)
  
  

  Most of the preliminary versions of the more recent papers can be found on the arxiv

  Preprints and publications (preliminary versions before refereeing, with misprints and possibly mistakes):

• The speed of a random front for stochastic reaction-diffusion equations with strong noise (with C. Mueller and L. Mytnik), (pdf), Preprint, 2019.
• Global well-posedness for the Euler alignment system with mildly singular interactions (with J. An), (arxiv link), Preprint, 2019.
• Fluctuations of the KPZ equation in dimensions three and higher (with A. Dunlap, Y. Gu and O. Zeitouni), (arxiv link), Preprint, 2018.
• The random heat equation in dimensions three and higher: the homogenization viewpoint (with A. Dunlap, Y. Gu and O. Zeitouni), (arxiv link), Preprint, 2018.
• High frequency limit for a chain of harmonic oscillators with a point Langevin thermostat (with T. Komorowski, S. Olla, and H. Spohn), (arxiv link), Preprint, 2018.
• Fluctuations of random semi-linear advection equations (with Y. Gu and T. Komorowski), (pdf), Preprint, 2018.
• The Bramson delay in the non-local Fisher-KPP equation (with E. Bouin and C. Henderson), (pdf), Preprint, 2017.
• The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher (with Y. Gu and O. Zeitouni), (pdf), Preprint, 2017.
• The Schroedinger equation with spatial white noise: the average wave function (with Y. Gu and T. Komorowski), (pdf), Preprint, 2017.
• Global regularity for the fractional Euler alignment system (with T. Do, A. Kiselev and C. Tan), (pdf), Preprint, 2017.
• The weak coupling limit for the random Schrödinger equation: The average wave function (with T. Chen and T. Komorowski), (pdf), Preprint, 2017.
• The Bramson logarithmic delay in the cane toads equations (with E. Bouin and C. Henderson),(pdf), Preprint, 2016.
• Refined long time asymptotics for the Fisher-KPP fronts (with J. Nolen and J.-M. Roquejoffre), (pdf), Preprint, 2016.
• Convergence to a single wave in the Fisher-KPP equation (with J. Nolen and J.-M. Roquejoffre), (pdf), Preprint, 2016.
• Super-linear spreading in local and non-local cane toads equations (with E. Bouin and C. Henderson),(pdf), Preprint, 2015.
• Radiative transfer with long-range interactions: regularity and asymptotics (with C. Gomez and O. Pinaud), (pdf), Preprint, 2015.
• Finite time singularity for the modified SQG patch equation (with A. Kiselev, Y. Yao and A. Zlatos), (pdf), Preprint, 2015.
• The random Schroedinger equation: slowly decorrelating time-dependent potentials (with Y. Gu), (pdf), Preprint, 2015.
• The random Schroedinger equation: homogenization in time-dependent potentials (with Y. Gu), (pdf), Preprint, 2015.
• Hypoelliptic estimates in radiative transfer (with C. Gomez and O. Pinaud), (pdf), Preprint, 2015.
• Anisotropic interactions in an aggregation model (with J.H.M. Evers and R. Fetecau), (pdf), Preprint, 2014.
• Exploring the effects of social preference, economic disparity, and heterogeneous environments on segregation (with N. Rodriguez), (pdf), Preprint, 2014.
• Precursors for Waves in Random Media (with G. Bal O. Pinaud and K. Solna), (pdf), Preprint, 2013.
• On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds (with Francois Hamel), (pdf), Preprint, 2013.
• Power-like delay in time inhomogeneous Fisher-KPP equations (with J. Nolen and J.-M. Roquejoffre), (pdf), Preprint, 2013.
• Homogenization driven by a fractional Brownian motion: the shear layer case (with T. Komorowski and A. Novikov), (pdf), Preprint, 2013.
• The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity (with I. Kukavica and Mi. Ignatova), (pdf), Preprint, 2013.
• Long time energy transfer in the random Schroedinger equation (with T. Komorowski), (pdf), Preprint, 2013.
• Traveling wave solutions in a reaction-diffusion model for criminal activity, (with H. Berestycki and N. Rodriguez), (pdf), Preprint, 2012.
• Wave-like solutions for nonlocal reaction-diffusion equations: a toy model (with G. Nadin, B. Perthame and L. Rossi) (pdf), to appear in Math. Mod. Nat. Phenom., 2013.
• The logarithmic delay of KPP fronts in a periodic medium (with F. Hamel, J. Nolen and J.-M. Roquejoffre), (pdf), Preprint, 2012.
• The Harnack inequality for second-order elliptic equations with divergence-free drifts (with I. Kukavica and M. Ignatova), (pdf), to appear in Comm. Math. Sci., 2013.
• A short proof of the logarithmic Bramson correction in Fisher-KPP equations (with F. Hamel, J. Nolen and J.-M. Roquejoffre), (pdf), to appear in Net. Heter. Med., 2013.
• Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case (with A. Kiselev), (pdf), to appear in Jour. Math. Phys., 2013.
• Asymptotics of the solutions of the stochastic lattice wave equation (with T. Komorowski and S. Olla), (pdf), to appear in Arch. Rat. Mech. Anal., 2013.
• A differential equations approach to l_1-minimization with applications to array imaging (with M. Moscoso, A. Novikov and G. Papanicolaou), (pdf), Inverse Problems, 28, 2012, 1050012012.
• From homogenization to averaging in cellular flows (with G. Iyer, T. Komorowski and A. Novikov), (pdf), Preprint, 2011.
• Evolution of particle separation in slowly decorrelating velocity fields (with T. Komorowski and A. Novikov), (pdf), Comm. Math. Sci., 10, 2012, 767--786.
• Biomixing by chemotaxis and enhancement of biological reactions (with A. Kiselev), (pdf), Comm. PDEs, 37, 2012, 298--318.
• Existence and non-existence of Fisher-KPP transition fronts (with J. Nolen, J.-M. Roquejoffre and A. Zlatos), (pdf), Arch. Rat. Mech. Anal., 203, 2012, 217--246.
• Kinetic limits for waves in a random medium (with G. Bal and T. Komorowski), (pdf), Kinet. Relat. Models 3, 2010, 529-644.
• A sharp bound on the L^2 norm of the solution of a random elliptic dierence equation (with T. Komorowski), (pdf, to appear in Comm. Math. Sci., 2011.
• Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential (with T. Komorowski), (pdf), Discr. Cont. Dyn. Sys. B, 17, 2012, 871--914
• A sharp bound on the $L^2$ norm of the solution of a random elliptic difference equation (with T. Komorowski), (pdf), Comm. Math. Sci., 9, 2011, 607--622.
• A simple model for asset price bubble formation and collapse (with A. Kiselev), (pdf), Preprint, 2010.
• Exit times for diffusions with incompressible drifts (with G. Iyer, A. Novikov and A. Zlatos), (pdf), SIAM J. Math. Anal. {42}, 2010, 2484--2498.
• Asymptotics of the phase of the solutions of the random Schr\"odinger equation (with G. Bal and T. Komorowski), (pdf), Arch. Ration. Mech. Anal. 200, 2011, 613--664.
• The non-local Fisher-KPP equation: traveling waves and steady states (with H. Berestycki, G. Nadin and B. Perthame), (pdf), Nonlinearity, 22, 2009, 2813--2844.
• Limit of fluctuations of solutions of Wigner Equation (with T. Komorowski and Sz. Peszat), (pdf), Communications in Mathematical Physics, 292, 2009, 479-510
• Travelling fronts for the thermodiffusive system with arbitrary Lewis numbers (with F. Hamel), (pdf), Archive for Rational Mechanics and Analysis, 195, 2010, 923--952.
• Stability of generalized transitions fronts (with A. Mellet, J, Nolen and J.-M. Roquejoffre), (pdf), Communications in PDE, {\bf 34}, 2009, 521--552.
• The explosion problem in a flow (with H. Berestycki, A. Kiselev and A. Novikov), (pdf), Journal d'Analyse Math\'ematique, 110, 2010, 31--65.
• Traveling waves in a one-dimensional random medium (with J. Nolen), (pdf), to appear in Ann. de l'Inst. Henri Poincare, C. Analyse non lineaire, 2009.
• Propagation and quenching in a reactive Burgers-Boussinesq system (with P. Constantin, J.-M. Roquejoffre and N. Vladimirova), (pdf), Nonlinearity, 21, 2008, 221--271.
• Traveling waves for the Keller-Segel system with Fisher birth terms (with G. Nadin and B. Perthame), (pdf), Interfaces and Free Boundaries, 10, 2008, 517-538.
• On asymptotics of a tracer advected in a locally self-similar, correlated flow (with T. Komorowski), (pdf), Asymptotic Analysis, 53, 2007, 159--187.
• Relaxation in reactive flows, (with P. Constantin and A. Novikov), (pdf), Geometric and Functional Analysis, 18, 2008, 1145-1167.
• KPP pulsating front speed-up by flows, (with A. Zlatos), (pdf), Communications in Mathematical Sciences, 5, 2007, 575-593.
• Moderate dispersion in scalar conservation laws (with B. Perthame), (pdf), Communications in Mathematical Sciences, 5, 2007, 473-484.
• Self-averaging from lateral diversity in the Ito-Schroedinger equation, (with G. Papanicolaou and K. Solna), (pdf), Multiscale Modeling and Simulation, 6, 2007, 468--492.
• Passive tracer in a slowly decorrelating random flow with a large mean, (with T. Komorowski), (pdf), Nonlinearity, 20, 2007, 1215-1239.
• Traveling waves in 2D reactive Boussinesq systems with no-slip boundary conditions, (with P. Constantin and M. Lewicka), (pdf), Nonlinearity, 19, 2006, 2605-2615.
• Diffusion and Mixing in a Fluid Flow, (with P. Constantin, A. Kiselev and A. Zlatos),(pdf), Annals of Mathematics, 68, 2008, 643--674..
• Wave field correlations in weakly mismatched random media (with G. Bal), (pdf), Stochastics and Dynamics, 2006, 301-328.
• Existence of pulsating waves in a model of flames in sprays (with P. Constantin, K. Domelevo and J.-M. Roquejoffre), (pdf), Journal of the European Mathematical Society, 8, 2006, 555--584.
• The stochastic acceleration problem in two dimensions (with T. Komorowski), (pdf), Israel Journal of Mathematics, 155, 2006, 157--204.
• Non-adiabatic KPP fronts with an arbitrary Lewis number (with F. Hamel), (pdf), Nonlinearity, 18, 2005, 2881-2902.
• Bounds on the speed of propagation of the KPP fronts in a cellular flow (with A. Novikov), (pdf), Archive for Rational Mechanics and Analysis, 184, 2007, 23--48.
• Flame capturing with an advection-reaction-diffusion model (with N. Vladimirova and G. Weirs), (ps), Combustion Theory and Modeling, 10, 2006, 727-747.
• Traveling fronts in porous media: existence and a singular limit (with P. Gordon), (pdf), Proceedings of the Royal Society London A, 462, 2006, 1965-1985.
• Diffusion in a weakly random Hamiltonian flow (with T. Komorowski), (pdf), Communications in Mathematical Physics, 263, 2006, 277-323.
• Quenching of reaction by cellular flows (with A. Fannjiang and A. Kiselev), (pdf), Geometric and Functional Analysis, 16, 2006, 40-69.
• The quantum scattering limit for a regularized Wigner equation (with B. Perthame), (pdf), Methods and Applications of Analysis, 11, 2004, 447-464.
• Non-Planar Fronts in Boussinesq Reactive Flows (with H. Berestycki and P. Constantin), (pdf), Ann. de l'Inst. Henri Poincar\'e, C. Analyse non lin\'eaire, 23, 2006, 407-437.
• The KPP system in a periodic flow with a heat loss (with P. Gordon and N. Vladimirova), (ps,pdf ), Nonlinearity, 18, 2005, 571-589.
• Quenching and propagation in KPP reaction-diffusion equations with a heat loss (with H. Berestycki, F. Hamel and A. Kiselev), (pdf), Archive for Rational Mechanics and Analysis, 178, 2005, 57-80.
• Stability of time reversed waves in changing media (with G. Bal), (pdf), Discrete and Continuous Dynamical Systems A, 12, 2005, 793 - 815.
• Time splitting for the Liouville equation in a random medium (with G. Bal), (pdf), Communications in Mathematical Sciences, 3, 2004, 515 - 534.
• Boundary layers for cellular flows at high Peclet numbers (with A. Novikov and G. Papanicolaou), (ps,pdf)), Communications in Pure and Applied Mathematics, 58, 2005, 867-922.
• Exponential decay for the fragmentation or cell-division equation (with B. Perthame), (pdf), Journal of the Differential Equations, 210, 2005, 155-177.
• Time splitting for wave equations in random media (with G. Bal), (pdf), Model. Math. Anal. Num. (M2AN), 38, 2004, 961-987.
• Flame Enhancement and Quenching in Fluid Flows (with N. Vladimirova, P. Constantin, A. Kiselev and O. Ruchaiskiy), (ps), Combustion Theory and Modeling, 7, 2003, 487 - 508.
• Fronts in reactive convection: bounds, stability and instability (with P. Constantin and A. Kiselev), (ps), Communications in Pure and Applied Mathematics, 56, 2003, 1781-1803.
• Self-averaging of Wigner transforms in random media (with G. Bal and T. Komorowski), (ps), Communications in Mathematical Physics, 242, 2003, 81-135.
• Statistical stability in time reversal (with G. Papanicolaou and K. Solna), (ps), SIAM Journal of Applied Mathematics, 64, 2004, 1133-1155.
• Stability in a nonlinear population maturation model (with S. Mischler and B. Perthame) (ps), M3AS (Mathematical Models & Methods in Applied Science), 12, 2002, 1751-1772.
• Self-averaging in time reversal for the parabolic wave equation (with G. Bal and G. Papanicolaou), (ps), Stochastics and Dynamics, 2, 2002, 507-531.
• The parabolic wave approximation and time reversal (with G. Papanicolaou and K. Solna), (ps), Matematica Contemporanea, 23, 2002, 139-159.
• Time reversal and refocusing in random media (with G. Bal), (ps), SIAM Journal of Applied Mathematics, 63, 2003, 1475-1498.
• Radiative transport limit for the random Schroedinger equation (with G. Bal and G. Papanicolaou), (ps), Nonlinearity, 15, 2002, 513-529.
• Time Reversal for Classical Waves in Random Media (with G. Bal), (ps), Comptes rendus de l'Academies Sciences - Serie I/Mathematique, 333, 2001, 1041-1046.
• Wave transport for a scalar model of the Love waves (with G. Bal), (ps), Wave Motion, 36, 2002, 49-66.
• An upper bound for the bulk burning rate for systems (with A. Kiselev), (ps), Nonlinearity, 14, 2001, 1297-1310.
• Quenching of flames by fluid advection (with P. Constantin and A. Kiselev), (ps), Communications in Pure and Applied Mathematics, 54, 2001, 1320--1342.
• Enhancement of the traveling front speeds in reaction-diffusion equations with advection (with A. Kiselev), (ps), Ann. de l'Inst. Henri Poincar\'e, C. Analyse non lin\'eaire, 18, 2001, 309--358.
• Wave transport along surfaces with random impedance (with G. Bal, V. Freilikher and G. Papanicolaou), (ps) Physical Review B, 62, 2000, 6228-6240.
• Bulk burning rate in passive - reactive diffusion (with P. Constantin, A. Kiselev and A. Oberman), (ps), Archive for Rational Mechanics, 154, 2000, 53-91.
• Probabilistic theory of transport processes with polarization (with G.Bal and G.Papanicolaou), (ps) SIAM Journal of Applied Mathematics, 60, 2000, 1639 - 1666.
  
• Radiative Transfer of Sound Waves in a Random Flow: Turbulent Scattering and Mode-Coupling (with A.Fannjiang), (ps), SIAM Journal of Applied Mathematics, 61, 2001, 1545-1577.
  
• Diffusive energy scattering from weakly random surfaces (with G.Bal and G.Papanicolaou), (ps), Journal of Mathematical Physics, 40, 1999, 4813-4827.
• Diffusion approximation of radiative transfer problems with interfaces (with G.Bal), (ps)SIAM Journal of Applied Mathematics, 60, 2000, 1887-1912.
  
• Transport theory for acoustic waves with reflection and transmission at interfaces (with G.Bal, J.B.Keller and G.Papanicoalou), (ps), Wave Motion, 30, 1999, 303-327.
  
• Level sets in turbulent front propagation (with P.Constantin and A.Kiselev), (ps), Preprint, 1998.
  
• Radiative transport in a periodic structure (with G.Bal, A.Fannjiang and G.Papanicolaou), (ps), Journal of Statistical Physics 95 (1/2):479-494, 1999.
• Waves and transport (with G.Papanicolaou), IAS/Park City Mathematics Series, Vol. 5, L. Caffarelli and Weinan E, eds., AMS, 1998, pp. 305-382.
• Evolution of trajectories correlations in steady random flows (with A.Fannjiang and G.Papanicolaou) (ps).
  In `Proceedings of Symposia in Applied Mathematics', Volume 54, R. Spigler and S. Venakides editors, American Mathematical Society, (1998), 105-130.
• Transport equations for waves in a half space (with J.Keller and G.Papanicolaou) (ps).
  Comm. PDE's, 22, (1997), 1869-1910.
• Transport equations for elastic and other waves in random media (with J.Keller and G.Papanicolaou) (ps). Wave Motion 24, (1996), 327-370
  
• Stability of the P to S energy ratio in the diffusive regime (with George Papanicolaou and Joseph B. Keller) (ps). Bulletin of the Seismological Society of America 86, (1996), 1107-1115. Erratum. 86, (1996), p. 1997.
• On the complete algebra of symmetries of integrable systems (with E.Schulman), Theor. Math. Phys. 95, 1993, 387-392.

Grants

• NSF grant DMS-9971742 "Radiative transport theory for waves", August 1999-August 2002.
• ONR grant N00014-02-1-0089 "Time-Reversal for Waves in Random Media", November 2001-2004.
• Alfred P. Sloan Research Fellowship, 2002-2004.
• NSF grant DMS-0203537 ``Propagation of fronts and waves in complex media'', 2002-2005.
• DARPA-ONR grant N00014-04-1-0224 "Time Reversal for Electromagnetic Waves in Random Media", 2004-2009.
• NSF grant DMS-0604687 ``The Kinetic Theory of Waves and Reactive-Diffusive Fronts'', 2006-2009.
• NSF FRG grant DMS-0854952 "Stochastics and Dynamics: Asymptotic problems", 2009-2012.
• NSF grant DMS-0908507 "Waves and Fronts in Heterogeneous Media", 2009-2012.
• AFOSR NSSEFF Fellowship, 2010-2015.
• NSF FRG grant DMS-115893, "Singularities, mixing and long time behavior in nonlinear evolution", 2012-2015.
• NSF grant DMS-1311903, "Waves, Particle Transport and Fronts in Heterogeneous Media".

Links

Here are some links related to Israel. Here are some links related to Classical Music.

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Lenya Ryzhik ( ryzhik@math.stanford.edu)